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The  Directly=Useful 


Technical  Series 


FOUNDED  BY  THE  LATE  WILFRID  J.  LINEHAM,  B.Sc.,  M.Inst.C.E. 


THE  THEORY 


PRACTICE 


OF 


AEROPLANE  DESIGN 


BY 


S.  T.  G.  ANDREWS,  B.Sc.  (Engineering),  London 

Member  of  the  Institute  of  Aeronautical  Engineers, 
Consulting  Engineer ; 


AND 


S.  F.  BENSON,  B.Sc.  (Engineering),  London 

Whitworth  Exhibitioner, 

Member  of  the  Royal  Aeronautical  Society, 

Consulting  Engineer, 


NEW  YORK 

E.  P.  BUTTON  &-  COMPANY 

68 1    FIFTH   AVENUE 
I92O 


13,  8 


TL  A  ?/ 

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At 


PRINTED    BY   STRANGEWAYS   AND   SONS,    TOWER   STREET, 
CAMBRIDGE   CIRCUS,    LONDON,    ENGLAND. 


EDITORIAL  NOTE 

THE  DIRECTLY- USEFUL  TECHNICAL  SERIES  requires  a  few  words 
by  way  of  introduction.  Technical  books  of  the  past  have  arranged 
themselves  largely  under  two  sections  :  the  Theoretical  and  the 
Practical.  Theoretical  books  have  been  written  more  for  the 
training  of  college  students  than  for  the  supply  of  information  to 
men  in  practice,  and  have  been  greatly  filled  with  problems  of  an 
academic  character.  Practical  books  have  often  sought  the  other 
extreme,  omitting  the  scientific  basis  upon  which  all  good  practice 
is  built,  whether  discernible  or  not.  The  present  series  is  intended 
to  occupy  a  midway  position.  The  information,  the  problems  and 
the  exercises  are  to  be  of  a  directly-useful  character,  but  must  at 
the  same  time  be  wedded  to  that  proper  amount  of  scientific 
explanation  which  alone  will  satisfy  the  inquiring  mind.  We 
shall  thus  appeal  to  all  technical  people  throughout  the  land, 
either  students  or  those  in  actual  practice. 


425504 


AUTHORS'  PREFACE 

THE  need  of  a  reliable  text-book  in  the  theory  and  practice 
of  aeroplane  design-  has  long4  been  recognised  by  all  those  con- 
nected with  aeronautical  affairs.  The  present  volume  aims  at 
supplying  this  want  and  will  be  found  useful  by  designers,  aero- 
nautical draughtsmen,  and  students,  besides  containing  much  of 
interest  to  the  general  reader. 

The  study  of  Aeronautics  can  only  be  successfully  attempted 
by  those  possessing  a  good  knowledge  of  Mathematics  and 
Physics.  Aeroplanes  are  machines  containing  many  differing 
elements.  These  elements  demand  a  great  or  less  knowledge 
of  scientific  matters  according  to  their  nature.  In  order  to  be- 
come an  aeronautical  engineer  and  designer  it  is  necessary  to 
have  a  thorough  knowledge  of — 

(A)  The  Graphic  Representation  of  Laws.      From  the  practical 
point  of  view  graphs  are  essential  to  the  designer  and  engineer. 
Visualisation  of  the  relationships  existing  between  certain  quanti- 
ties, as  for  example    Lift    (Drag,  or   Lift/Drag),   with   change   in 
the  Angle  of   Incidence,   is   of  the    utmost    importance.      Graphs 
exhibit  the  variation  of  one  quantity  with  another  far  more  power- 
fully than  any  other  method  known.     Again,  the  reverse  process, 
namely,    the    establishing    of   an    algebraical    equation    to    satisfy 
the    relationship    existing    between    quantities    whose    graph    has 
been  drawn,  is  of  considerable  use  in  original  work. 

(B)  The  fundamental  Theorems  in  Theoretical  Mechanics  such 
as    those    dealing   with   velocity,    acceleration,    gravity,   moments 
of    inertia,    centrifugal    force,    fluid     motion,    work,    energy,    and 
power. 

(c)  Various  Theorems  in  Applied  Mechanics.  The  more  im- 
portant of  these  are  considered  in  their  bearing  upon  aeronautical 
problems  in  Chapters  II.  and  IV.,  and  at  other  places  as  occasion 
demands. 

As  will  be  seen  from  even  a  casual  glance  through  this  book, 
more  than  usual  care  has  been  devoted  throughout  to  the  pre- 

vii 


viii  AUTHORS'   PREFACE 

paration  and  production  of  the  diagrams  and  tables,  and  it  is 
confidently  anticipated  that  they  will  prove  of  direct  utility  to 
those  actively  engaged  in  aeroplane  design.  A  special  feature 
has  also  been  made  of  illustrative  examples,  and  a  large  number 
of  these  will  be  found  scattered  throughout  the  text.  It  is  hoped 
that  their  insertion  will  clear  up  all  doubtful  points.  Furthermore, 
the  whole  subject  has  been  presented  in  a  complete  and  logical 
manner,  and  the  principles  enunciated  have  been  applied  in 
Chapter  XIII.  to  the  lay-out  of  a  complete  machine. 

The  authors  desire  to  thank  the  following  :  Messrs.  Vickers, 
who  have  spared  no  pains  in  supplying-  information  and  photo- 
graphs relating  to  their  machines  ;  Flight,  for  their  unfailing 
courtesy  at  all  times,  and  permission  to  use  the  several  blocks 
indicated  in  the  text  ;  Messrs.  Handley  Page,  Ltd.  ;  Boulton  & 
Paul ;  Edgar  Allen  &  Co.,  and  Brunton's,  for  photographs  and 
information  where  indicated  ;  Messrs.  Barling  &  Webb,  for 
permission  to  use  the  tapered  strut  formula  ;  and  to  the  Advisory 
Committee  for  Aeronautics  for  permission  to  make  extracts  from 
their  reports.  In  this  connection  we  might  add  that  we  are  still 
awaiting  the  photographs  which  the  Secretary  of  the  National 
Physical  Laboratory  promised  in  August,  1919. 

We  should  also  like  to  express  our  thanks  to  Miss  G.  E. 
Powers,  Cambridge  Mathematical  Tripos ;  Mr.  Lewis  Curtis, 
M.A. ;  and  Mr.  H.  J.  Cardnell-Harper,  A.M.I.C.E.,  for  reading 
through  the  proofs  ;  and  to  Mr.  A.  B.  Tomkins,  for  assistance 
in  preparing  some  of  the  illustrations. 

In  conclusion,  while  every  precaution  has  been  taken  to  guard 
against  errors,  the  authors  would  be  glad  of  notification  of  any 
which  may  be  observed,  or  suggestions  for  improvements  in 
future  editions. 

S.  T.  G.  ANDREWS, 
S.   F.   BENSON. 


So  Shakespeare  Crescent, 

Manor  Park,  London,  E.  12. 
January,  1920. 


CONTENTS 


CHAPTER   I 

PAGE. 

THE  PRINCIPLES  OF  DESIGN  ......          i 

The  characteristics  of  an  aeroplane  —  Weight  —  Aerofoil  characteristics — 
The  resistance  of  the  machine  —  Horse-power  available  at  the  airscrew — 
Controllability  and  stability — General  consideration  of  design. 


CHAPTER    II 
THE  MATERIALS  OF  DESIGN 13 

Timber -Light  alloys — Steel — Aeroplane  fabric — Stress,  strain,  elasticity 
—Tests  —  Factor  of  safety  —  Wind  pressure  —  Stress  diagrams  —  Method 
of  sections. 

CHAPTER    III 
THE  PROPERTIES  OF  AEROFOILS 38 

• 

Wind  tunnel  investigation — The  N.P.L.  four-foot  tunnel — The  balance — 
The  Eiffel  laboratory — The  flat  plate — The  inclined  flat  plate— Flat  plate 
moving  edgewise —The  aerofoil — Pressure  distribution  over  an  aerofoil — 
Aerofoil  efficiency  —  Pressure  distribution  over  the  entire  surface  of  an 
aerofoil  —  Full-scale  pressure  distribution  experiments  —  Aspect  ratio  — 
The  relative  importance  of  the  upper  and  lower  surfaces  of  an  aerofoil — 
Determination  of  the  lift  and  drag  of  a  series  of  aerofoils  with  plain  lower 
surface  and  variable  camber  of  upper  surface — Determination  of  the  lift 
and  drag  of  a  series  of  aerofoils  with  the  same  upper  surface  and  variable 
camber  of  lower  surface — Determination  of  the  lift  and  drag  of  a  series  of 
aerofoils,  the  position  of  the  maximum  ordinate  being  varied  —  Effect  of 
thickening  the  leading  edge  of  an  aerofoil  —  Effect  of  thickening  the  trail- 
ing edge  of  an  aerofoil  —  Centre  of  pressure  —  Reflexed  curvature  towards 
the  trailing  edge — Interference  of  aerofoils — Gap — Decalage — Stagger — 
The  choice  of  an  aerofoil — Units — The  law  of  similitude — Standard  wing 
sections. 

ix 


x  CONTENTS 

CHAPTER    IV 

PAGE 

STRESSES  AND  STRAINS  IN  AEROPLANE  COMPONENTS       .         .      101 

Moments  of  inertia — Shear  force  and  bending  moment — Stresses  in  beams 
— Relation  between  load,  shear,  bending  moment,  slope,  and  deflection — 
Struts — Eccentric  loading — Streamlined  struts — Tapered  streamline  struts. 

CHAPTER   V 
DESIGN  OF  THE  WINGS  .         .         .         .         .         .         .         .130 

Wing  structures — Monoplane  trusses — Biplane  trusses — Wireless  biplane 
trusses  —  Strutless  biplane  truss  —  Triplane  trusses  —  Wireless  triplane 
trusses — Quadruplane  trusses — Drag  and  incidence  bracing — Development 
of  the  single  lift  truss — Tractor  and  pusher  machines — The  factor  of  safety 
—  Experimental  investigation  of  the  stresses  upon  a  full-size  machine 
during  flight—  Stresses  —  Stresses  in  the  wing  structure  —  Wing  loading — 
Wing  weights  —  Stresses  due  to  downloading  —  Stressing  of  the  wing 
structure  —  General  procedure  for  design  of  the  members  of  the  wing 
structure  —  Change  of  direction  of  drag  forces  in  the  wing  structure  — 
Stagger — Detail  design  of  the  wing  structure — The  external  bracing — The 
interplane  struts — Tapered  strut  formula — The  drag  struts  and  bracing — 
Design  of  the  spars — Practical  example  of  wing  structure  design — Design 
of  the  wing  ribs — Wing  assembly. 


CHAPTER   VI 
RESISTANCE  AND  STREAMLINING 208 

Resistance — Variation  from  the  (V2)  law — Streamlining — Inclination  of 
struts — Resistance  cf  the  body  or  fuselage — Aeroplane  bodies — Deperdussin 
monocoque  fuselages — B.E.  2  and  B.E.  3  fuselages — Resistance  of  wires — 
Resistance  of  flat  plates — Resistance  of  landing  gear — Effect  of  airscrew 
slip  stream— Resistance  of  complete  machine— Experimental  Measure- 
ment of  the  resistance  of  full-size  machines — Skin  friction. 


CHAPTER   VII 
DESIGN  OF  THE  FUSELAGE .     238 

Weights — The  fuselage— Stressing  the   fuselage — Design    of  the   engine 
mountings — Gyroscopic  action  of  a  rotary  engine  and  the  airscrew. 


CONTENTS  xi 

CHAPTER   VIII 

PAGE 

DESIGN  OF  THE  CHASSIS 260 

Function  of  the  chassis— Forces  on  chassis  when  landing — Method  of 
locating  fore  and  aft  position  of  chassis— General  principles  of  chassis 
design — Types  of  chassis — Stresses  in  chassis  members — Shock  absorbers 
— The  tail  skid — Streamlining  the  chassis. 

CHAPTER   IX 
DESIGN  OF  T,HE  AIRSCREW      .......     280 

Methods  of  design — Experimental  method  of  design — Tractive  power 
developed  at  the  airscrew — Design  of  the  airscrew  by  the  blade  element 
theory — Stresses  in  airscrew  blades — Stresses  due  to  bending — The  con- 
struction of  an  airscrew. 

CHAPTER   X 
STABILITY 303 

Definition — Stability  nomenclature — The  equations  of  motion — The  resist- 
ance and  rotary  derivatives — Longitudinal  stability  of  the  Bleriot  machine — 
Lateral  stability  of  the  Bleriot  model— Longitudinal  stability  of  a  biplane. 

CHAPTER   XI 
DESIGN  OF  THE  CONTROL  SURFACES 346 

Controllability  and  stability — The  tail  plane  and  elevator — Reduction  of 
effectiveness  of  the  tail  plane  due  to  wash  from  the  main  planes — The 
elevator — Tail  plane  design — Determination  of  dimensions  of  the  tail  plane 
and  settings  of  the  elevator — Fin  and  rudder  lateral  force  due  to  the 
airscrew — Ailerons  or  wing  flaps — Balance  of  the  control  surfaces — 
Construction  of  control  surfaces. 

CHAPTER   XII 

PERFORMANCE "...       .     381 

t 

Definition — The  resistance  of  the  machine — Horse-power  required — 
Horse-power  available — Rate  of  climb  —  Performance  calculations — 
Measurement  of  performance — The  airspeed  indicator  (anemometer) — 
Performance  tests  on  full-scale  machines — Rate  of  climb  test — Theory 
of  the  aneroid  barometer — Measurement  of  rate  of  climb. 


xii  CONTENTS 

CHAPTER   XIII 

PAGE 

GENERAL  LAY-OUT  OF  MACHINES    .         .         .         .         .         ;     403 

The  process  of  laying-out — General  arrangement. 

CHAPTER   XIV 

THE  GENERAL  TREND  OF  AEROPLANE  DESIGN        .         .         .     424 

-.. 

The  Bleriot  machine  —  Avro  machines — Airco  machines — Armstrong- 
Whitworth  machines— Bristol  machines — Handley  Page  machines— Sop- 
with  machines — Vickers  machines — Boulton  &  Paul  machines — Official 
machines — Wing  design — Fuselages — Control  surfaces — The  airscrew — 
Performance. 


THE  THEORY  &  PRACTICE 


OF 


AEROPLANE   DESIGN. 


CHAPTER   I. 
THE  PRINCIPLES  OF  DESIGN. 

The  Characteristics  of  an  Aeroplane. — Practical  flying  is 
of  very  recent  date,  since  it  was  only  in  1903  that  the  Wright 
Brothers,  in  an  aeroplane  weighing  750  Ibs.  and  mounting  a 
i6h.p.  engine,  succeeded  in  leaving  the  ground. 

The  work  of  the  Wright  Brothers  is  particularly  interesting 
and  instructive  to  the  aeronautical  student  and  engineer.  They 
first  of  all  learnt  how  to  '  fly  '  a  biplane  glider — that  is  the  wing 
structure  only  of  an  aeroplane — by  launching  themselves  from  the 
top  of  a  slope  (see  Fig.  I,  p.  8).  In  this  way  they  discovered 
practically  the  elements  of  stability,  and  it  is  noteworthy  that  in 
their  machines  the  controlling  surface  to  give  longitudinal  stability 
was  placed  in  front  of  the  wing  structure  (see  Figs.  I  and  2,  p.  8), 
whereas  modern  practice  places  this  member  (the  tail  plane)  at 
the  rear.  Another  important  detail  in  connection  with  the  work 
of  the  Wright  Brothers  was  the  fact  that  they  adopted  the  prin- 
ciple of  warping  the  wings  in  order  to  maintain  stability  and  do 
away  with  the  necessity  of  moving  their  bodies  on  the  glider,  the 
method  used  by  Lilienthal  and  Chanute.  They  also  realised  the 
fundamental  basis  of  mechanical  flight,  namely,  that  the  problem 
of  the  aeroplane  is  largely  one  of  strength  in  relation  to  weight. 
There  being  no  suitable  power  plant  available  combining  the 
advantages  of  light  weight  with  maximum  power,  they  designed 
a  special  motor  to  fulfil  these  requirements,  and  this  can  justly 
be  called  the  forerunner  of  modern  aero  engines. 

The  work  of  these  pioneers,  therefore,  is  an  excellent  example 
of  the  necessity  for  linking  together  into  one  homogeneous  whole 
technical  and  scientific  research. 


2  AEROPLANE    DESIGN 

To  adjust  the  many  details  which  enter  into  the  design  of  a 
successful  machine  is  a  matter  of  compromise,  and  requires  con- 
siderable care  and  judgment  on  the  part  of  the  designer.  It  is 
possible  to-day  to  predict  with  considerable  accuracy  the  per- 
formance of  a  machine  before  it  leaves  the  ground  ;  and  in  this 
connection  Table  I.,  dealing  with  a  machine  constructed  in  1912, 
is  instructive  and  worthy  of  notice. 

TABLE  I. — COMPARISON  OF  CALCULATED  AND  ACTUAL 
PERFORMANCE. 

Calculated.          Actual. 

Maximum  speed  ...       68        ...       69       miles  per  hour. 

Minimum  speed  ...      39' 5     ...       39-5    miles  per  hour. 

Rate  of  climb 430       ...  400-450  feet  per  minute. 

Minimum  gliding  angle  i  in  8*4    ...    i  in  7*4 

The  problem  before  the  manufacturer  to-day  is  to  supply, 
on  a  commercial  basis,  a  machine  which  will  carry  a  definite 
useful  load  over  a  given  distance.  The  nature  of  this  problem 
will  be  fully  discussed  in  subsequent  chapters.  For  a  given 
type  of  machine  the  designer  has  to  balance  various  conflicting 
factors  so  that  the  resulting  machine  may  fulfil  certain  definite 
conditions  with  regard  to  efficiency,  strength,  stability,  and 
convenience.  For  example,  if  a  fast  Scout  is  required,  the  reduc- 
tion of  resistance  is  a  prime  factor,  and  stream-lining  must  be 
carefully  considered  in  all  exposed  parts.  Again,  if  a  cargo- 
carrying  machine  is  wanted,  great  lifting  capacity  is  necessary, 
and  the  choice  of  a  suitable  aerofoil  is  essential ;  for  which 
purpose  the  designer  must  use  the  latest  research  work  of  the 
aeronautical  laboratories. 

There  are,  however,  common  to  all  types  of  machines  certain 
basic  considerations,  namely : 

Weight. 

Aerofoil  characteristics. 

Resistance. 

Horse-power  available  at  the  airscrew. 

Controllability  and  stability. 

Weight. — The  question  of  weight  is  obviously  an  important 
one,  and  since  a  reduction  in  weight  will  always  lead  to  improved 
performance,  it  will  be  useful  to  indicate  in  which  directions  a 
designer  may  hope  to  effect  a  saving.  The  necessity  for  obtain- 
ing maximum  strength  with  a  minimum  of  weight  is  one  of  the 
fundamental  problems  of  aeroplane  construction.  In  no  branch 


THE    PRINCIPLES    OF    DESIGN  3 

of  engineering  is  it  more  essential  that  weight  should  be 
economically  distributed.  The  weight  of  an  aeroplane  can  be 
considered  under  the  following  headings  : 

(a)  Weight  of  the  structural  portion  of  the  machine. 

(b)  Weight  of  the  power  plant,  fuel,  lubricant,  etc. 

(c)  Weight  of  the  useful  load. 

With  present  types  of  machines  and  constructional  methods 
it  is  found  that  the  weight  of  the  structural  portion  amounts  to 
about  one-third  of  the  total  weight  of  the  machine.  The  follow- 
ing figures,  giving  the  weights  of  the  principal  elements  of  the 
aeroplane  structure  as  a  percentage  of  its  total  weight,  are 
representative  of  modern  practice. 

TABLE  II. — WEIGHTS  OF  STRUCTURAL  COMPONENTS  EXPRESSED 
AS  PERCENTAGES  OF  THE  TOTAL  WEIGHT. 

Wing  structure  complete        i3°/o  of  total  weight. 

Body  complete  ...  13%       »»  » 

Tail  unit  complete      ...         ...         ...         2°/0       ,,  „ 

Landing  gear 4°/0       „  „ 

It  is  not  likely  that  much  improvement  can  be  made  on  the 
above  figures  unless  some  other  material,  possessing  greater 
strength  per  unit  weight  than  wood,  is  made  available. 

The  relative  proportions  of  weight  of  power  plant  and  useful 
load  are  necessarily  dependent  to  a  large  extent  upon  the  purpose 
for  which  the  machine  is  to  be  used.  The  greater  the  flying  range 
required  the  greater  will  be  the  quantity  of  fuel,  lubricant,  etc., 
required,  and  the  smaller  will  be  the  useful  load.  Considering 
the  power  plant,  it  is  useful  to  note  the  enormous  advances 
which  have  been  made  in  recent  years  in  reducing  the  weight 
per  horse-power  of  aero  engines.  Table  III.  illustrates  this 
reduction. 

TABLE  III. — DIMINUTION  IN  WEIGHT  PER  H.P. 
OF  AERO  ENGINES. 

Year  ...    1901     1905     1908    1910     1912     1913 

Wt/H.P.   ...  127  ...  9-5  ...  5-2  ...  57  ...  5-3  ...  47 

Year  ...    1914    1915     1916    1917     1918     1919 
Wt/H.P.   ...   3-9  ...  3-85...  3-1  ...  2'8  ...  i'9  ...  l'5 

Aerofoil  Characteristics.— In  Chapter  III.  we  shall  study 
the  various  characteristics  of  an  aerofoil  in  detail,  and  show  how 
to  determine  the  aerofoil  which  is  most  suitable  for  a  given  set 


4  AEROPLANE    DESIGN 

of  conditions  ;  and  it  is  therefore  sufficient  for  our  present  pur- 
pose to  consider  briefly  the  variation  in  section,  form,  number  of 
surfaces  used,  and  arrangement  of  those  surfaces  in  relation  to 
each  other. 

It  is  desirable  to  use  a  wing  section  with  the  maximum 
vertical  reaction  (or  Lift)  combined  with  a  minimum  horizontal 
reaction  (or  Drag)  ;  in  other  words,  the  Lift/Drag  ratio  must  be 
high.  The  Wright  Brothers,  in  their  early  machines,  used  a 
wing  section  with  a  Lift/Drag  ratio  of  12,  and  this  figure  repre- 
sented a  very  great  improvement  on  previous  wing  sections. 
To-day  many  aerofoils  have  a  Lift/Drag  ratio  of  17,  and  in 
some  cases  this  figure  has  been  exceeded.  But  these  results 
have  been  obtained  partly  at  the  expense  of  the  maximum 
lift  coefficient,  and  consequently  for  a  given  minimum  speed 
we  require  a  larger  surface  to  support  a  given  weight  than 
with  a  section  of  lower  maximum  Lift/Drag  ratio,  but  higher 
maximum  lift  coefficient.  It  will  be  instructive,  and  will  serve 
to  impress  these  facts  more  clearly  on  the  mind  if  we  study 
them  with  reference  to  the  fundamental  equation  for  the  lifting 
capacity  of  a  machine,  namely  — 


Formula  i 


Where  W    =  the  total  weight  lifted. 

Ky  =  the  absolute  lift  coefficient. 

(0      =  the  density  of  the  air  in  Ibs.  per  cubic  foot. 

A    =  the  area  of  the  supporting  surface  in  square  feet. 

V    =  the  velocity  of  the  machine  in  feet  per  second. 

g     =  the  acceleration  due  to  gravity. 

A  heavier-than-air  machine  will  not  leave  the  ground  until 
the  above  relationship  is  satisfied.  Hence  for  machines  with 
equal  supporting  areas,  the  larger  the  maximum  value  of  Ky  for 
the  wing  section  the  smaller  will  be  the  value  of  V  at  which  the 
machine  leaves  the  ground,  and  the  smaller  will  be  the  landing 
speed.  Conversely,  if  the  landing  speed  of  two  machines  with 
aerofoils  of  different  maximum  lift  coefficient  be  the  same,  then 
the  machine  with  the  wing  section  of  lower  maximum  lift  co- 
efficient must  have  the  larger  area  of  supporting  surface.  A 
little  time  spent  in  examining  this  equation  and  its  various 
factors  will  help  to  bring  these  points  out,  and  will  be  time  well 
spent. 

It  is  desirable  that  a  machine  should  have  as  large  a  speed 
range  as  possible,  and  be  capable  of  landing  at  a  comparatively 
low  speed,  so  that  the  sacrifice  of  a  high  lift  coefficient  in  order 


THE    PRINCIPLES    OF    DESIGN  5 

to  obtain  a  better  L/D  ratio  is  not  altogether  an  advantage. 
It  is  possible  that  some  practical  means  of  varying  the  camber 
of  the  wing  section  will  be  devised  in  the  future,  and  this  would 
furnish  the  best  solution  to  the  problem.  Attempts  have  al- 
ready been  made  in  this  direction,  but  the  results  have  not 
justified  the  increased  weight  and  complication  of  parts. 

The  planes  are  generally  made  rectangular  in  form,  and  this 
brings  us  to  a  consideration  of  aspect  ratio,  which  is  the  ratio 
span  :  chord.  The  higher  the  aspect  ratio,  the  better  will  be  the 
L/D  ratio  of  a  plane.  In  Chapter  III.  it  is  shown  that  when 
the  aspect  ratio  is  diminished  from  8  to  3,  there  is  a  diminu- 
tion of  35%  in  the  maximum  value  of  the  L/D  ratio.  This 
is  due  to  the  lateral  escape  of  the  air  at  the  wing-tips,  which 
causes  a  loss  of  lift,  together  with  a  large  increase  in  the 
drag.  This  is  an  inherent  defect  of  the  modern  wing 
section,  and  is  very  difficult  to  remedy.  By  suitably  shaping 
the  outer  ends  of  the  planes  it  is  possible  to  reduce  this  loss 
considerably.  It  has  been  noted  above  that  increase  of  aspect 
ratio  means  an  improved  L/D  ratio  over  the  wing.  Unfor- 
tunately, however,  increase  of  aspect  ratio  means  increased 
mechanical  difficulties  in  the  construction  of  the  wing  structure, 
heavier  wings  and  bracing,  resulting  in  increased  resistance. 
Moreover,  the  controllability  of  the  machine  and  its  ability  to 
manoeuvre  rapidly  will  be  diminished  :  hence  it  is  necessary 
to  compromise,  and  the  aspect  ratio  of  an  aeroplane  is  there- 
fore generally  from  5  to  8.  With  increasing  size  of  machine, 
the  ratio  appears  to  be  advancing  slightly,  and  in  some  cases 
approaches  a  value  of  10 ;  but  this  is  quite  unusual,  and  it  is 
doubtful  whether  there  is  any  advantage  to  be  derived  from 
it.  This  consideration  of  aspect  ratio  leads  us  on  to  another 
important  consideration,  namely,  the  arrangement  of  surfaces. 
Modern  aeroplanes  may  be  classified  according  to  the  number 
of  the  supporting  surfaces  :  thus  we  have  monoplanes,  biplanes, 
triplanes,  &c.,  but  of  these  it  may  be  said  that  the  biplane  group 
is  by  far  the  most  important  and  numerous,  and  the  tractor 
biplane  is  the  form  of  aeroplane  which  at  present  approaches 
the  nearest  to  a  standardised  type.  It  may  be  said  generally 
that  the  most  efficient  plane  from  an  aerodynamical  point  of 
view  is  the  monoplane,  for  there  is  no  possibility  of  interference 
of  the  planes  as  there  is  on  the  other  types,  and  for  smaH 
machines  this  is  probably  the  best  arrangement.  With  increas- 
ing size  and  weight,  however,  the  large  span  required  in  this 
type  to  give  the  necessary  supporting  surface  means  a  relatively 
heavy  wing  and  increased  complication  of  bracing,  leading  to  a 
large  increase  in  structural  resistance ;  hence,  for  all  but  small 


6  AEROPLANE   DESIGN 

machines,  the  multiplane  arrangement  is  more  efficient.  Pre- 
cisely the  same  argument  holds  with  reference  to  the  biplane 
and  triplane.  For  the  size  and  weight  of  the  machines  most 
generally  used  to-day  the  biplane  arrangement  is  undoubtedly 
the  most  efficient  one,  but  as  the  demand  for  larger  and  heavier 
machines  increases,  and  particularly  for  the  passenger  and  cargo- 
carrying  machines,  which  will  be  increasingly  developed  in  the 
near  future,  the  triplane  will  become  a  serious  competitor,  and 
may  prove  to  be  a  more  efficient  arrangement.  Apart  from 
this  point  of  view,  the  difficulty  of  handling  and  housing  a 
great  structure  of  100  feet  span  or  more  will  become  an  im- 
portant factor.  In  this  connection,  however,  the  practice  of 
folding  back  the  wings  of  a  machine  when  not  in  use  (as  shown 
in  Fig.  3,  p.  8)  will  to  some  extent  obviate  this  difficulty.  It  must 
also  be  remembered  that  it  is  relatively  cheaper  to  increase  the 
depth  of  a  hangar  than  it  is  to  increase  its  span. 

The  Resistance  of  the  Machine. — This  is  usually  regarded 
as  made  up  of  two  parts — 

1.  The  drift  or  drag  of  the  wings. 

2.  The  resistance  of  the  remainder  of  the  machine. 

The  first  part  will  be  very  fully  considered  in  Chapter  III., 
and  it  therefore  remains  to  say  a  few  words  with  reference  to  the 
second  part.  The  first  designer  to  enclose  the  body  from  the 
wings  to  the  tail  plane  was  Nieuport,  in  1909,  and  by  this  means 
he  obtained  a  considerable  improvement  in  speed  without  any 
corresponding  increase  in  the  horse-power  used.  All  modern 
machines  are  stream-lined  to  the  utmost  possible  extent,  result- 
ing in  a  great  reduction  in  the  total  resistance  of  the  exposed 
external  parts.  Table  IV.  gives  the  average  resistances  of  the 
component  parts  of  machines  in  general  use  to-day. 

TABLE  IV. — PERCENTAGE  RESISTANCES  OF  AEROPLANE 

COMPONENTS.  Percentage. 

Body      60 

Landing  gear    ...          ...          ...          ...          ...          ...  17 

Tail  unit  complete        8 

Lift  bracing  and  external  fittings         ...         ...         ...  15 

As  will  be  seen,  the  body  accounts  for  the  major  portion  of 
the  total  resistance  of  the  machine,  and  it  is  impossible  to  avoid 
this  with  the  usual  arrangement  of  the  radiator.  Some  German 
machines  have  had  their  radiators  fixed  in  the  surface  of  the  top 
plane. 


THE    PRINCIPLES    OF    DESIGN  7 

Horse-power  available  at  the  Airscrew — The  function 
of  the  airscrew  is  to  transform  the  torque  on  the  engine  crank- 
shaft into  a  propulsive  thrust  by  discharging  backwards  the  air 
through  which  it  moves  ;  and  whose  resultant  reaction  enables 
the  necessary  forward  momentum  to  be  secured.  The  horse- 
power available  at  the  airscrew,  therefore,  depends  upon  the 
horse-power  of  the  engine,  the  efficiency  of  the  airscrew,  and  the 
efficiency  of  the  transmission  between  the  engine  and  the  air- 
screw. The  first  two  of  these  factors  are  largely  influenced  by 
the  density  of  the  air  in  which  they  are  operating,  and  it 
is,  therefore,  desirable  to  say  a  few  words  concerning  the 
effect  of  variation  in  altitude  upon  the  performance  of  an 
aeroplane. 

It  is  generally  known  that  the  density  of  the  atmosphere 
diminishes  with  increase  of  altitude,  the  weight  of  a  cubic  foot 
of  air  at  15,000  feet  being  only  "59  of  the  weight  of  an  equal 
volume  at  sea-level.  What  effect  will  this  change  of  density 
have  upon  an  aeroplane  flying  at  this  altitude  ?  Considering, 
first,  the  power  plant,  it  is  found  from  the  laws  of  thermo- 
dynamics that  the  power  developed  is  directly  proportional  to 
the  weight  of  the  fuel  burned  per  cycle,  which  weight  in  its 
turn  depends  upon  the  supply  of  oxygen  available.  Since  the 
percentage  of  oxygen  present  in  the  atmosphere  remains 
practically  constant  at  all  densities,  it  follows  at  once  that  the 
amount  of  oxygen  available  at  15,000  feet  will  only  be  '59  of 
the  quantity  available  at  sea-level.  Hence  the  combustion  of 
fuel  per  cycle  and  the  horse-power  developed  at  this  altitude 
will  be  in  the  same  proportion.  Therefore,  increase  in  altitude 
will  tend  to  a  corresponding  decrease  in  the  horse-power 
developed,  unless  special  devices  have  been  incorporated  in  the 
engine. 

The  diminution  in  density  also  affects  the  resultant  air 
pressure  upon  the  wing  surface  and  the  body  of  the  machine. 
Reference  to  the  fundamental  equation  for  lifting  capacity 
shows  that  the  Lift  is  directly  proportional  to  the  density  of 
the  air.  It  is,  therefore,  apparent  that  a  diminution  of  the 
density  (p)  means  a  reduced  lifting  capacity  of  the  wings. 
Similarly  the  horizontal  component  of  the  resultant  air  force, 
that  is  the  Drag,  will  be  reduced  to  '59  of  its  value  at  ground- 
level  ;  and  at  first  sight  it  would  therefore  appear  that  the 
forward  speed  of  the  machine  would  be  maintained.  It  is  here, 
however,  that  the  diminished  lifting  capacity  of  the  planes  steps 
in  to  modify  the  result.  Since  the  horse-power  has  diminished 
in  the  same  ratio  as  the  drag,  it  will  be  impossible  to  obtain  the 
increased  lift  necessary  to  support  the  weight  of  the  machine  by 


8  AEROPLANE   DESIGN 

flying  at  a  higher  speed,  and  it  is  therefore  necessary  to  alter 
the  flight  attitude  of  the  machine.  The  increased  lift  obtained 
by  flying  at  a  larger  angle  of  incidence  will  be  accompanied  by 
an  increase  in  the  drag  of  the  wing  surface,  and  hence  the  total 
drag  of  the  machine  will  be  greater  than  "59  of  its  value  at 
ground-level.  As  a  result,  the  machine  will  fly  at  a  somewhat 
slower  speed  at  altitude  than  at  ground-level.  The  reduction  in 
speed  will  necessitate  a  further  slight  change  in  attitude  of  the 
machine  until  the  reaction  of  the  wings  is  just  equal  to  the 
weight,  and  horizontal  flight  will  then  be  possible. 

Following  this  argument  through,  it  will  be  seen  that  there 
will  come  a  time  when  the  machine  is  flying  at  the  wing  attitude 
which  gives  the  maximum  lift — corresponding  to  the  critical 
angle  of  the  aerofoil  section — and  therefore  is  unable  to  obtain 
an  increase  in  reaction  by  alteration  of  attitude.  Consequently 
at  this  stage  it  will  be  impossible  to  reach  a  higher  altitude,  and 
this  height  is  known  as  the  'ceiling  height'  or  'ceiling'  of  the 
machine.  This  altitude  varies  considerably  with  different 
types  of  machines,  the  maximum  height  reached  up  to  the 
moment  being  in  the  neighbourhood  of  30,000  feet.  For  the 
majority  of  machines,  however,  20,000  feet  is  a  more  usual 
'  ceiling.' 

The  efficiency  of  transmission  depends  upon  the  form  which 
is  employed.  If  a  short  shaft  running  in  roller  bearings  is  used, 
very  little  loss  will  occur  between  the  engine  and  the  airscrew, 
while  a  longer  shaft  will  absorb  somewhat  greater  power  on 
account  of  the  increase  in  the  number  of  bearings.  If  the 
airscrew  is  geared  down,  as  is  frequently  the  case  nowadays, 
there  may  be  a  considerable  loss  of  power  depending  upon  the 
efficiency  of  the  gear  employed. 

From  a  consideration  of  the  variation  of  the  horse-power 
developed  by  the  engine  we  turn  to  discuss  the  question  of 
airscrew  efficiency.  The  performance  to  be  expected  from  an 
airscrew  is  dependent  upon  several  factors,  the  chief  being  the 
engine  and  the  machine  to  which  the  screw  is  fitted,  and  these 
factors  should  be  considered  when  designing  the  airscrew.  To 
illustrate  these  factors,  consider  an  airscrew  coupled  to  an 
engine  of  insufficient  power  to  drive  it.  The  resistance  offered 
to  rotation  by  the  airscrew  will  be  so  great  that  the  engine  will 
be  unable  to  develop  its  normal  number  of  revolutions  and 
consequently  it  will  develop  less  power  than  it  is  capable 
of  reaching  under  correct  conditions.  As  will  be  seen  in 
Chapter  IX.,  the  efficiency  of  an  airscrew  is  proportional  to 
its  effective  pitch,  the  latter  quantity  being  directly  propor- 
tional to  the  forward  speed.  An  airscrew  to  exert  its  maximum 


FIG.  i.— The  Wright  Glider. 


FIG.  2. — The  Wright  Biplane. 


Reproduced  by  courtesy  of  Messrs.  Hand  ley  Page,  Ltd. 

FIG.  3. — Method  of  folding  Back  Wings  of  a  large  Machine 
for  Storage  Purposes. 

Facing  page  8. 


THE    PRINCIPLES    OF    DESIGN  9 

efficiency  must  be  correctly  designed  in  itself,  and  must  also 
work  under  the  conditions  for  which  it  is  designed.  A  reduction 
in  speed,  such  as  occurs  during  climbing,  will  therefore  lead  to 
diminished  efficiency.  The  angle  of  attack  of  the  blade  sections 
is  fixed  in  accordance  with  the  conditions  for  which  it  is  desired 
to  have  maximum  efficiency,  and  any  departure  from  these 
conditions  will  alter  the  most  efficient  angle  of  the  blade 
sections.  Unfortunately  the  airscrew  must  operate  under  widely 
varying  conditions  during  flight,  and  therefore  cannot  always 
be  working  at  maximum  efficiency.  For  instance,  the  variation 
in  density  with  altitude  has  a  similar  effect  upon  the  airscrew 
blade  as  it  has  upon  the  wing  surfaces.  Moreover,  whereas  in 
horizontal  flight  the  whole  of  the  lift  is  provided  by  the 
supporting  surfaces,  in  climbing  the  airscrew  thrust  also  con- 
tributes to  the  lift,  that  is,  it  takes  part  of  the  weight  of  the 
machine.  An  extreme  case  is  shown  in  Fig.  4,  p.  16.  The  thrust 
under  these  conditions  will  reach  a  maximum  value,  and  the 
engine,  being  very  heavily  loaded,  will  tend  to  go  slower, 
resulting  in  a  further  decrease  in  airscrew  efficiency.  The 
efficiency  of  an  airscrew  when  working  under  the  best  con- 
ditions may  reach  as  high  a  figure  as  85%,  but  in  climbing  it  is 
more  frequently  in  the  neighbourhood  of  65%.  If  it  were 
possible  to  adjust  the  angle  of  the  sections  in  accordance  with 
the  speed  of  flight  in  a  similar  easy  way  to  the  manner  in  which 
the  angle  of  incidence  of  the  planes  can  be  altered,  the  efficiency 
of  the  airscrew  could  be  maintained  at  its  maximum  value  under 
all  conditions.  Attempts  have  been  made  to  realise  this  result 
by  pivoting  the  blades  so  that  they  may  be  rotated  about  a 
radial  axis,  thereby  permitting  the  angle  of  attack  of  the 
sections  to  be  varied  with  relation  to  the  axis  of  the  screw 
itself.  Up  to  the  present  time  these  efforts  have  achieved  only 
moderate  success,  but  there  is  little  doubt  that  the  problem  will 
be  satisfactorily  solved  in  the  future. 

Controllability  and  Stability. — There  are  four  forces  acting 
on  an  aeroplane  in  flight : 

1.  Its  weight  acting  downwards  through  the  centre 

of  gravity         ...         ...         ...         ...         ...    W 

2.  The  lift  of  the  supporting  surfaces  acting  at  the 

centre  of  pressure        ...          ...          ...         ...     L 

3.  The  resistance   of  the    machine   acting   at   the 

centre  of  resistance    ...         ...         ...         ...     R 

4.  The  thrust  of  the  airscrew  T 


10 


AEROPLANE   DESIGN 


The  distribution  of  these  forces  is  shown  diagrammatically 
in  Fig.  5  below,  and  it  is  upon  the  way  in  which  these  varying 
quantities  are  disposed  that  the  success  or  failure  of  the 
machine  depends. 

The  weight  of  the  macm'ne  does  not  remain  constant  through- 
out a  flight  because  of  the  fuel  consumption  of  the  engine,  and 
in  the  case  of  a  bombing  or  a  cargo-carrying  machine  the  release 
of  the  bombs  or  discharge  of  the  cargo  produces  a  further  varia- 
tion. Wherever  possible,  the  varying  weights,  such  as  the  oil  and 
petrol,  etc.,  should  be  so  arranged  that  the  position  of  the  C.G.  of 


FIG.  5. — Equilibrium  of  an  Aeroplane  in  Flight. 

the  machine  remains  unaltered.  A  further  point  to  be  noted  is 
that  the  weights  should  be  concentrated  as  much  as  possible,  in 
order  to  reduce  the  moment  of  inertia  of  the  machine,  and  thus 
allow  of  easy  controllability.  The  lift  of  the  supporting  surfaces 
is  equal  to  the  weight  of  the  machine  in  horizontal  flight,  but  the 
position  at  which  the  resultant  lift  acts  varies  over  a  considerable 
range.  The  C.P.  of  a  modern  aerofoil  travels,  within  the  range 
of  flying  angles,  from  about  "3  to  '6  of  the  chord  from  the  leading 
edge,  and  hence,  while  it  is  possible  to  obtain  the  C.P.  of  the 
wing  and  the  C.G.  of  the  weights  in  line  with  each  other  for  one 
particular  angle  of  incidence,  yet  for  all  the  other  angles  there 
will  be  a  weight/lift  moment  set  up  tending  to  produce  a  nose 
dive  or  a  tail  dive  according  as  the  C.P.  is  behind  or  in  front  of 
the  C.G.  In  order  to  produce  a  restoring  couple  an  auxiliary 
lift  surface  must  be  introduced,  and  this  function  is  carried  out 
by  the  tail  unit.  By  raising  or  depressing  the  elevator  a  couple 
is  produced  tending  to  restore  equilibrium.  The  tail  plane  fulfils 


THE    PRINCIPLES    OF   DESIGN  n 

a  similar  purpose  in  producing  equilibrium  when  the  line  of 
thrust  of  the  airscrew  does  not  coincide  with  that  of  the  total 
resistance  of  the  machine.  The  position  of  the  centre  of  resist- 
ance of  the  machine  travels  up  and  down  in  a  vertical  direction 
with  variation  of  speed.  This  is  due  to  the  fact  that  at  normal 
flying  .angles  the  drag  of  the  wings  remains  almost  constant 
over  a  considerable  range  of  speed.  The  resistance  of  the 
remainder  of  the  machine  varies  directly  with  the  speed,  and 
hence  the  resultant  of  the  two  will  vary  in  its  point  of  appli- 
cation. 

The  general  question  of  controllability  and  stability  has 
received  much  more  attention  in  England  during  recent  years 
than  on  the  Continent  or  in  America.  The  mathematical  side 
of  this  problem  has  been  developed  by  Bryan,  and  the  practical 
application  of  Bryan's  results  has  been  demonstrated  by  Bair- 
stow's  work  at  the  National  Physical  Laboratory.  It  is  now 
possible,  as  a  result  of  their  work,  to  design  a  machine  with  any 
required  degree  of  controllability  or  stability.  Here,  as  in  so 
many  of  the  problems  connected  with  Aeronautics,  compromise 
is  frequently  necessary.  If  a  machine  is  very  responsive  to  the 
control  lever  it  is  not  generally  stable,  while  if  a  machine  pos- 
sesses a  large  amount  of  static  stability  it  is  heavy  on  the 
controls.  The  stability  of  an  aeroplane  is  considered  when  the 
machine  is  in  its  normal  flying  attitude.  It  frequently  happens, 
however,  that  when  banking  or  performing  some  other  evolution 
the  wings  assume  a  position  approaching  the  vertical.  When 
this  is  the  case,  the  functions  of  the  controlling  surfaces  are 
interchanged.  There  is  need  of  extended  investigation  as  to 
the  effect  of  such  reversion  upon  the  behaviour  of  the  machine. 

Machines  in  the  early  days  of  aeronautics  broke  their  backs 
under  the  strain  of  a  sudden  change  in  the  direction  of  the 
flight  path,  and  experiments  have  since  been  made  to  determine 
the  increased  loads  likely  to  be  encountered  when  doing  sharply 
banked  turns  or  loops.  It  has  been  found  that  the  load  is 
frequently  increased  to  three  or  four  times  the  normal,  while 
even  an  ordinary  banked  turn  will,  under  certain  conditions,  al- 
most double  the  load.  This  brings  us  to  a  brief  consideration  of 
the  factor  of  safety.  Since  fighting  machines  must  be  able  to 
manoeuvre  rapidly,  it  is  obvious  that  they  must  be  strongly 
built,  and  they  are  not  considered  tolerably  safe  unless  the 
wings  can  support  at  least  six  times  the  weight  of  the  aeroplane. 
This  question  of  the  factor  of  safety  makes  large  demands  upon 
the  resourcefulness  of  the  designer,  for  he  must  obtain  strength 
combined  with  minimum  weight,  and  must  therefore  design  his 
members  as  economically  as  possible,  and  yet  retain  sufficient 


12  AEROPLANE    DESIGN 

material  to  carry  the  stresses.  With  large  machines  a  lower 
factor  of  safety  can  be  allowed,  as  there  is  not  such  a  likelihood 
of  sudden  loads  being  thrown  upon  the  members,  and  this  will 
have  an  important  bearing  upon  the  possibilities  of  passenger 
and  cargo-carrying  machines.  In  fact,  for  commercial  purposes 
generally  a  small  machine  will  be  of  little  use,  and  it  is  probable 
that  the  tendency  of  aeroplane  design  will  be  towards  a  machine 
considerably  larger  than  those  in  most  frequent  use  to-day,  and 
hence  the  question  of  weight- saving  will  become  increasingly 
important  because  of  the  inherent  tendency  of  the  weight  to 
increase  faster  than  the  area  of  the  supporting  surfaces.  This 
tendency  may  be  simply  explained  as  follows.  For  two  aero- 
plane structures  geometrically  similar  the  stresses  resulting  from 
an  equal  rate  of  loading  will  be  similar.  The  weight  of  such 
structures  will  increase  as  the  cube  of  the  similar  dimensions, 
while  the  supporting  area  will  increase  only  as  the  square  of  the 
similar  dimension,  so  that  the  ratio  of  the  weight  to  the  sup- 
porting surface  will  increase  as  the  linear  dimension,  and  thus  a 
definite  limit  would  appear  to  be  placed  upon  the  size  to  which 
an  aeroplane  can  be  built. 

General  Consideration  of  Design. — The  general  method 
of  procedure  in  designing  an  aeroplane  can  now  be  briefly  out- 
lined. A  clear  conception  is  necessary  of  the  functions  that  the 
completed  machine  has  to  fulfil.  An  aerofoil  must  then  be 
selected  giving  the  necessary  coefficients  at  the  required  speeds. 
A  general  arrangement  of  the  machine  should  then  be  laid  out 
and  a  preliminary  balance  effected.  The  total  resistance  of  the 
machine  can  be  estimated  and  an  investigation  made  into  the 
question  of  horse-power  available  at  the  airscrew.  The  amount 
of  controllability  and  stability  can  next  be  decided  and  the 
areas  of  the  controlling  surfaces  fixed.  Details  can  be  inserted 
in  the  design  and  the  various  performance  curves  drawn  out  for 
the  machine.  During  construction  the  designer  should  check 
his  estimated  figures  as  opportunity  offers,  and  revise  his  design 
accordingly.  If  this  procedure  be  followed  he  will  be  able  to 
predict  the  actual  performance  of  his  machine  with  reasonable 
certainty. 


CHAPTER  II. 
THE  MATERIALS  OF  DESIGN. 

THE  materials  best  suited  for  aeronautical  purposes  must 
combine  strength  with  light  weight.  At  the  moment  timber  is 
the  main  material  used,  but  research  work  has  led  to  the  rapid 
development  of  some  very  light  alloys  which  are  proving  serious 
competitors  to  wood. 

Timber. — Until  the  last  few  years  little  research  work  had 
been  done  upon  this  material  of  design,  but  much  attention  and 
scientific  thought  has  been  devoted  to  it  recently,  ai)d  more 
especially  to  the  question  of  artificial  seasoning.  In  former 
times  natural  seasoning  was  the  chief  method  in  vogue,  but  the 
speeding-up  of  production  and  the  ever-increasing  demand  for 
all  varieties  of  timber  has  led  to  great  developments  in  artificial 
processes  of  seasoning.  Green  or  unseasoned  timber  has  only 
about  80%  of  the  strength  of  dry  or  seasoned  timber.  There  is 
great  danger,  however,  that  unless  artificial  seasoning  is  scientifi- 
cally controlled,  the  process  will  be  carried  too  far,  with  the 
result  that  certain  varieties  of  timber — chiefly  the  coniferous 
varieties — will  be  rendered  brittle.  Age  has  a  very  similar  effect 
upon  mahogany  and  beech. 

Wood  varies  in  weight  per  cubic  foot,  that  is  in  its  density, 
according  to  its  variety ;  the  portion  of  the  tree  from  which  it  is 
cut ;  the  time  of  the  year  at  which  it  is  cut ;  and  the  amount  of 
seasoning.  Even  after  seasoning,  which  determines  the  amount 
of  moisture  present,  variations  occur  according  to  the  amount  of 
protection  upon  the  surface  of  the  wood,  which  allows  of  or  pre- 
vents the  wood  from  absorbing  moisture  from  the  atmosphere 
or  elsewhere. 

As  a  general  rule,  the  wood  from  the  top  portion  of  the  bole 
is  about  5%  lighter  than  that  from  the  bottom'  portion.  In 
seasoning  the  wood  shrinks  considerably  in  width  (some  4% 
to  8%),  but  very  little  in  length.  The  percentage  amount  of 
moisture  present  in  any  given  sample  can  be  easily  estimated 
by  boring  a  hole  with  a  twist  bit  through  the  sample.  The 
borings  should  be  weighed  immediately,  and  then  slowly  heated 
in  a  crucible  over  a  sand  bath,  great  care  being  taken  to  see 
that  they  do  not  char.  When  thoroughly  dry  they  should  be 
weighed  again  without  removal  from  the  crucible,  and  the 
difference  in  the  weighings  enables  the  percentage  amount  of 
moisture  present  to  be  calculated. 


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THE    MATERIALS    OF  DESIGN  15 

Table  V.  gives  much  useful  and  practical  information  con- 
cerning the  most  important  timbers  of  commerce. 

Light  Alloys. — During  recent  years  several  light  alloys 
have  been  placed  on  the  market  for  which  the  makers  have 
made  various  claims  which  have  been  more  or  less  justified  in 
use.  The  properties  of  the  greatest  importance  in  a  light  alloy 
are  its  strength,  ductility,  and  permanence.  It  is  frequently 
found  that  an  alloy  possessing  great  strength  and  a  large  degree 
of  ductility  lacks  permanence.  One  of  the  most  frequent 
erroneous  claims  made  on  behalf  of  the  advertised  light  alloys 
is  in  connection  with  their  relative  density,  it  being  often  claimed 
that  the  density  is  less  than  that  of  pure  aluminium.  In  order 
to  obtain  such  a  result,  the  aluminium — the  basis  of  all  these 
light  alloys — must  have  been  alloyed  with  some  other  metal 
of  a  less  relative  density  than  aluminium.  Magnesium  seems 
to  be  the  only  likely  metal,  and  its  addition  to  aluminium, 
unless  in  a  very  small  percentage,  renders  the  resulting  alloy 
both  weak  and  brittle. 

Of  the  commercial  alloys,  Duralumin  is  the  best  known  and 
has  given  very  satisfactory  service.  Duralumin  is  composed  of 
aluminium,  copper  manganese,  and  magnesium  ;  variations  in 
composition  being  made  to  meet  particular  requirements.  The 
magnesium  contributes  to  the  hardness  of  the  alloy,  but  increases 
the  brittleness.  Duralumin  can  be  worked  hot  or  cold,  and  its 
chief  properties  are  given  in  Table  VI. 

TABLE  VI. — PROPERTIES  OF  DURALUMIN. 

Stress — Tons  per  square  inch. 
Rolled  bar.  Tubes.  Wire. 

Tensile 25  ...       25  ...       40 

Compressive      ...          ...       32 

Elongation         ,..         ...       2o°/o       ...       12^°  o         ..       2°/0 

Specific  gravity 277  to  2-84 

This  alloy  has  been  very  fully  tested  at  the  National  Physical 
Laboratory  by  Dr.  Rosenhain  and  Mr.  S.  L.  Archbutt  in  con- 
nection with  the  Alloys  Research  Committee  of  the  Institution 
of  Mechanical  Engineers.  In  their  report  they  introduce  the 
term  Specific  Tenacity,  which  is  the  constant  obtained  by 
dividing  the  tensile  strength  in  tons  per  square  inch  by  the 
weight  of  a  cubic  inch  in  pounds.  As  will  be  seen,  this  is  quite 
an  arbitrary  conception,  but  it  forms  a  very  useful  basis  for 
comparison,  and  apart  from  questions  of  ductility,  permanence, 
and  cost,  it  is  pointed  out  that  the  structural  value  of  any  alloy 


16  AEROPLANE    DESIGN 

or  other  material  is  proportional  to  its  specific  tenacity.     Using 
these  units,  the  values  shown  in  Table  VII.  have  been  obtained. 

TABLE  VII. — SPECIFIC  TENACITY  OF  DIFFERENT  MATERIALS. 

Material.  Specific 

Tenacity. 

Mild  carbon  steel          ...         ...         ...         ...  ...  105 

Special  heat-treated  steel         ...         ...         ...  ...  250 

N. P. L,  light  alloys        ...          ...          ...          ...  up  to  279 

Duralumin         ...          ...          ...          ...          ...  up  to  290 

Timber up  to  350 

Another  method  of  expressing  the  same  property  is  obtained 
by  using  the  length  of  the  bar  of  the  material,  which,  hanging 
vertically  downwards,  would  just  break  under  its  own  weight. 

The  use  of  these  alloys  for  purposes  connected  with  aircraft 
is  a  matter  of  great  discrimination,  as  their  properties  are  con- 
siderably affected  by  the  way  in  which  they  are  manipulated. 
Most  of  them  machine  easily,  and  are  capable  of  taking  quite 
a  high  polish.  It  may  be  noted  in  this  connection  that  when 
highly  polished  they  are  more  capable  of  resisting  corrosion 
than  when  left  rough.  It  should  also  be  remembered  that  all 
the  light  alloys  are  injured  by  high  temperatures,  so  that  they 
should  not,  unless  suitably  protected,  be  used  in  places  where 
they  will  be  exposed  to  great  heat,  as  near  the  engines,  exhaust 
pipes,  etc.  According  to  the  N.P.L.  report,  even  a  temperature 
of  200°  C.  reduces  the  strength  materially. 

In  working,  aluminium  the  temperatures  are  important.  If 
worked  when  too  hot  the  aluminium  becomes  too  soft,  while 
if  worked  too  cold  brittleness  results.  Cast  aluminium  is  popular, 
but  not  very  satisfactory.  Its  strength  is  only  about  five  tons 
per  square  inch,  and  there  is  very  little  elongation.  It  is  much 
more  useful  as  an  alloy. 

The  brass  or  gun-metal  alloys  are  formed  by  adding  tin, 
zinc,  and  small  quantities  of  other  elements  to  copper. 

Steel. — Steel  is  formed  from  iron  by  the  addition  of  carbon 
and  small  quantities  of  other  materials.  Mild  steel  has  a  tenacity 
of  under  26  tons  per  square  inch,  with  an  elongation  of  30%  on 
an  8"  gauge  length.  It  is  easy  to  get  a  strong  steel,  but  increase 
of  strength  generally  means  increase  of  brittleness.  Steel  may 
be  treated  by  heating  to  a  high  temperature  and  quenching  it  in 
oil.  Its  strength  is  increased  to  about  40  tons  per  square  inch 
by  the  addition  of  nickel,  with  but  little  loss  in  elongation. 
With  some  sacrifice  in  ductility  the  strength  may  be  further 
increased  to  between  50  and  60  tons  per  square  inch.  Chromium 


• 


FIG.  4. — Fokker  Biplane  '  Hanging  on  the  Prop.' 


A  stunt  evolved  by  Fokker  pilots  during  the  War.  To  an  observer  in 
another  machine  the  Fokker  has  the  appearance  of  remaining  stationary  in 
the  position  indicated  in  the  sketch.  It  is  probable,  however,  that  the 
aeroplane  is  losing  height  continuously,  the  airscrew  thrust  and  air  pressure 
being  sufficient  to  reduce  the  fall  to  very  small  dimensions,  as  this  position 
could  be  maintained  for  quite  long  periods.  The  Sopwith  '  Camel '  fitted 
with  a  Bentley  engine  can  assume  and  retain  a  similar  position. 


Facing  page  16. 


THE    MATERIALS    OF    DESIGN  17 

and  vanadium  are  also  largely  used  for  combining  with  steels  to 
form  high  tensile  strength  alloys.  When  rolled  into  thin  plates 
or  drawn  into  wire  the  ultimate  stress  is  still  further  increased, 
and  it  is  possible  to  produce  a  wire  TV'  in  diameter  with  a  break- 
ing stress  of  150  tons  per  square  inch.  High  tensile  steels 
should  not  be  subjected  to  punching  for  the  purposes  of  lighten- 
ing out,  as  the  loss  of  strength  may  amount  to  20° /c.  The  metals 
most  commonly  used  for  additions  in  making  steel  alloys  are 
aluminium,  chromium,  manganese,  molybdenum,  nickel,  tungsten, 
vanadium,  and  combinations  of  these  elements.  The  exact 
effect  produced  depends  upon  whether  they  are  added  singly  or 
in  combination.  Their  general  effect  is  given  below  : 

ALUMINIUM. — Usually  added  to  increase  the  fluidity  of  cast 
steel,  and  by  its  great  affinity  for  oxygen  to  reduce  the  formation 
of  oxides.  It  also  aids  in  the  prevention  of  blow-holes. 

CHROMIUM. — When  added  in  small  quantities  it  increases 
the  tensile  strength  of  the  steel,  but  when  added  in  large 
quantities  it  increases  the  brittleness.  It  is  largely  used  for 
projectiles,  railway  tyres,  and  springs. 

MANGANESE.  —  Added  to  make  self-hardening  steels.  In- 
creases the  tensile  strength  and  the  elongation. 

MOLYBDENUM. — Added  for  self-hardening  purposes.  Lowers 
the  melting  point  somewhat. 

NICKEL. — The  commonest  and  best-known  alloys  are  the 
nickel  steels.  An  addition  of  4%  nickel,  O'2°/0  carbon,  results  in 
an  increase  of  tensile  strength  of  about  10%  and  an  increase  in 
the  elastic  limit  of  about  25°/0.  This  increase  continues  with  the 
addition  of  more  nickel  until  the  quantity  of  nickel  present 
reaches  20%,  after  which  point  a  rapid  decrease  in  strength 
takes  place  with  the  addition  of  more  nickel.  Nickel  steels  offer 
great  resistance  to  corrosion,  but  when  more  than  ij°/0  °f  nickel 
is  present  these  steels  are  difficult  to  weld. 

TUNGSTEN.  —  Another  of  the  agents  for  obtaining  self- 
hardening  steels.  It  is  also  used  for  making  magnets.  Mushet 
steel — the  forerunner  of  the  modern  high-speed  steels — is  a 
tungsten  steel.  Tungsten  is  a  constituent  of  practically  all  the 
high-speed  tool  steels. 

VANADIUM,  generally  speaking,  increases  the  tensile 
strength  and  the  elastic  limit,  but  reduces  the  elongation  slightly. 

Table  VIII.  gives  the  chemical  composition  of  various 
steels  made  to  Air  Ministry  and  Engineering  Standards  Com- 
mittee specification,  by  Edgar  Allen  &  Co.,  of  Sheffield,  and 
shows  the  results  of  tests  upon  bars  i|"  in  diameter  turned 
down  to  the  British  Standard  test-piece  *  C.' 

c 


i8 


AEROPLANE    DESIGN 


TABLE  VIII.— STEELS  TO  STANDARD  SPECIFICATIONS. 


DESCRIPTION. 


SELECTED  AIR  MINISTRY 
STEELS. 

Si.     Part  2        

82.     H.T.  Alloy  bars 

88.     9  &  10.3%  Nickel 

814.  1 5 %Carbon  Case-hardening 

817.     5%  Nickel        „ 

819.     Chrome  Valve 

824.     Key  Steel  

826.     40-ton      

828.     loo-ton  Air-hardening  ... 

ENGINEERING  STANDARDS 
COMMITTEE'S  STEELS. 

E.S.C.  10.  Carbon  Case-harden'g 

E.S.C.  2%  Nickel         

E.S.C.  5%      „ 

E.S.C.  20%  Carbon       

E.S.C.  35%       » 

E.S.C.  3%  Nickel         

E.S.C.  ij%  Nickel  Chrome    ... 
E.S.C.  3%         „  „ 

E.S.C.    Air  hardening     Nickel 
Chrome 


CHEMICAL  COMPOSITION. 

Carbon. 

Silicon.    Manganese. 

Sulphur. 

Phos.          Nickel.             Chrome. 

i 

•25-'40 

•30       '4o-'85 

•06 

•06 

•28-'4o 

i  '5o--8o 

•04 

•04         3'0-4'Q            0-9-1-5 

— 

—           — 

•04 

•04         2-5-3-5 

'I2-'20 

0-5-1*0 

•04 

•04 

*IO-*20 

•10  -'40 

•04 

•04        4-50-6*0     ; 

•2-'4 

•50           -5 

•06 

•06                                  11-5-14-0 

•55--8o 

•8 

•04 

•04 

— 

'30--45 

•30       '5o-'8o 

•06 

•06           i  -o                -5 

'35- 

•50 

•035 

•035 

375-475  !     i  'o-r8 

•o8-'i4- 

'20                '60 

•04 

•04 

— 

— 

'IO-T5 

•3o       -25-'5o 

•05 

•05    i       2  '0-2  '5 

•i5 

'20                '40 

•05 

•05 

475-575  * 

•I5--25 

•25       '40--85 

•06 

•06 

— 

•30-40 

•30       '50--85 

•06 

•06 

— 

— 

'25-'35 

•30       '35-75 

•04 

•04 

275-3'5 

— 

j 

'25-'35 

•30       -35--6o 

•04 

•04        r25-I75 

075-1-21 

•20-  -30 

•30       '35--6o 

•04 

•04 

275-3-50 

0-45-0-7; 

'2S--36 

•30       -3  5  ~'6o 

•04 

•04 

3-50-4-50 

1-25-17; 

THE    MATERIALS    OF    DESIGN 


[EDGAR  ALLEN  &  Co. 


HEAT  TREATMENT. 

MECHANICAL  TESTS. 

Normalising 
or  hardening 
temperature. 

Tempering 
or  re-heating 
temperature. 

Max.  stress 
Condition.                 tons 
j     per  sq.  in. 

Yield 
point. 

Elong. 
%on 
2" 

Reduc. 
of  area 

I/od 
impact 
ft.  Ibs. 

BRINELL 
No. 

Degrees  Cent. 

Degrees  Cent. 

Tons  per 

sq.  in. 

840-880 

— 

— 

35 

20 

20 

40 

40 

— 

560-660 

Treated. 

55-65 

45 

18 

55 

40 

402 

840-880 

— 

Normalised. 

45 

32 

24 

5o 

— 

— 

— 

— 

Treated. 

38 

25 

20         55 

40 

— 

820-840 

740-760 

55 

65 

50 

13         40 

30 

— 

— 

— 

55 

40 

30 

18 

5o 

— 

— 

800-840 

— 

Normalised. 

55 

28 

Yield 

15 

45 

Red.& 

— 

— 

ratio. 

elong. 

820-870 

— 

Treated. 

40-50 

60 

22 

70 

30 

— 

790-830 

— 

• 

90-110 

— 

I3-6 

40-l6 

418-269 

— 

Yield 

ratio  % 

880-900 

750-770 

As  rolled. 

23-28 

50 

30 

50 

— 

92-112 

860-880 

750-770 

55 

25-35 

55 

30 

55 

— 

103-153 

820-840 

740-760 

55 

25-40 

60 

30 

55 

— 

103-179 

890-920 

H  — 

„ 

26-34 

5o 

28 

5o 

— 

105-149 

850-880 

— 

Treated. 

30-40 

5o 

25 

45 

I2I-I79 

840-880 

— 

55 

35-45 

55 

24 

45 

— 

I4O-202 

850 

600 

55 

45 

70 

15 

50 

— 

179 

820 

600 

» 

45 

75 

15 

5o 

— 

175 

820 

— 

„ 

100 

75 

5 

13 

— 

418     • 

2O 


AEROPLANE    DESIGN 


Aeroplane  Fabric. — This  is  cloth  of  a  fairly  closely  woven 
texture,  and  is  used  for  covering  the  wings,  fuselage,  and  tail 
structure.  The  strength  of  this  fabric  is  from  80  Ibs.  per  square 
inch  in  the  direction  of  the  warp  threads,  to  120  Ibs.  per  square 
inch  in  the  direction  of  the  weft  threads.  The  warp  threads  are 
those  running  longitudinally,  while  the  weft  threads  are  the 
shorter  ones  crossing  the  warp  threads  at  right  angles.  In 
order  to  make  this  fabric  taut,  air-tight,  and  unaffected  by 
moisture,  it  is  covered  with  *  dope.'  Dope  is  a  chemical  prepara- 
tion, the  base  of  which  is  cellulose  acetate,  and  from  four  to  five 
coats  are  applied,  the  result  being  to  increase  the  strength  of  the 
fabric  by  about  30%  as  well  as  rendering  it  weather-proof. 

Stress,  Strain,  Elasticity. — When  a  bar  of  ductile  material 
is  tested  in  tension  it  stretches,  and  at  first  this  stretching  is 
proportional  to  the  load  applied,  being  practically  uniform 
throughout  the  whole  length  of  the  bar.  This  proportionality 
of  elongation  to  load  is  known  as  Hooke's  Law,  and  continues 


mum  stress 


Compression 


Extension 


FIG.  6. — Stress  Strain  Diagram. 

up  to  a  point  known  as  the  elastic  limit.  At  a  load  a  little 
greater  than  the  elastic  limit  the  elongation  increases  more 
rapidly  than  the  load,  permanent  deformation  of  the  material 
occurs,  this  point  being  known  as  the  yield  point.  Further 


THE   MATERIALS  OF   DESIGN  21 

increase  of  the  load  brings  about  a  much  greater  increase  in  the 
elongation  up  to  the  maximum  load,  known  as  the  breaking 
load.  The  bar,  however,  does  not  immediately  break,  but  at  one 
point  a  *  waist  '  is  formed,  and  the  load  can  now  be  reduced 
while  the  elongation  continues,  due  to  the  reduction  in  the  cross- 
sectional  area  of  the  bar.  The  bar  finally  breaks  at  the  point 
where  the  waist  formed. 

Taking  rectangular  co-ordinates  as  in  Fig.  6,  the  relation 
between  stress  and  strain  can  be  plotted  as  shown.  It  should  be 
noted  that  this  figure  gives  the  nominal  stress  —  that  is,  the  stress 
upon  the  original  cross-sectional  area  of  the  bar. 

As  a  deduction  from  Hooke's  Law  we  have  the  relationship 

Modulus  of  Elasticity  =  Stress/Strain   ............  Formula  2 

When  a  bar  is  subjected  to  a  pull  in  one  direction,  there  is,  in 
addition  to  the  longitudinal  strain  in  the  direction  of  the  pull, 
a  transverse  strain  set  up  in  planes  at  right  angles  to  the  longi- 
tudinal strain,  resisting  the  change  in  length.  The  ratio  Trans- 
verse strain  /  Longitudinal  strain  is  within  the  elastic  limits  a 
constant  for  any  one  material,  and  is  known  as  Poisson's  ratio, 
being  frequently  denoted  by  the  Greek  letter  rj.  It  has  been 
suggested  that  Poisson's  ratio  is  a  constant  for  all  materials,  but 
recent  researches  have  shown  that  this  view  is  incorrect. 

From  Formula  2  the  various  Moduli  of  Elasticity  are  at  once 
derived,  namely  : 

Modulus    of    direct    tension    or    compression,    sometimes    called 

Young's  Modulus  .    Load/cross-sectional  area 

extension  or  compression  per  unit  length, 


or  E  =  —  ............  Formulas 

X 


Modulus  of  rigidity,   or  the  shear  modulus,  or  modulus  of  trans- 
verse elasticity  p 

=  G  =-— — — ^ Formula  4 

Unital  shear  strain 

Modulus  of  volume  or  the  bulk  modulus 

P 

=  K  =  — _ ^ ,_ Formula  5 

Unital  volume  strain 


22  AEROPLANE   DESIGN 

Transverse  strain  .   Formula  6 


Poisson's  Ratio  =   /? 


Longitudinal  strain 


The  relations  between  the  elastic  constants  are  best  re- 
membered in  the  following  forms : — 

j|  =  ^  +  ^  Formula  7 

•p 

p  =  2  (i  +  17)  Formula  8 

•p 

==  =  3(1-2  77)  Formula  9 

lv 

Tests. — The  general  method  employed  for  testing  the 
mechanical  properties  of  materials  is  to  cut  portions  from 
selected  pieces  and  to  turn  or  shape  them  to  standard  forms. 
These  pieces  are  then  tested  in  special  machines — the  nature 
of  the  test  depending  upon  the  purpose  for  which  the  material 
is  required.  From  the  results,  the  elastic  constants  of  the 
material  under  test  can  be  evaluated  by  means  of  the  formulae 
given  above. 

An  additional  method  of  testing,  which  is  being  increasingly 
adopted  in  practice  to-day,  is  known  as  the  Brinell  Hardness 
Test.  In  this  method  an  indentation  is  produced  in  the  flat 
surface  of  the  material  by  applying  a  constant  pressure  upon  it 
through  a  hardened  steel  ball.  The  diameter  of  the  indentation 
is  measured  and  the  hardness  is  taken  as  being  proportional  to 
the  area  of  the  cavity  made  by  a  ball  of  definite  size  when 
subjected  to  a  fixed  load.  The  size  of  the  ball  is  usually 
10  millimetres  in  diameter,  and  the  pressure  3000  kilograms. 

The  Brinell  Hardness  number  is  defined  as  the 

Total  load 


Curved  area  of  depression. 

It  is  possible  to  form  an  approximate  idea  of  the  tensile  strength 
of  a  material  from  a  knowledge  of  its  Brinell  Hardness  number, 
and  as  the  test  is  so  much  simpler  and  quicker  to  perform  than 
the  ordinary  tensile  test,  this  method  is  frequently  adopted  in 
cases  where  it  is  not  essential  to  have  very  accurate  data. 

Table  IX.  gives  the   Hardness   number  and  corresponding 
approximate  tensile  strength  of  various  qualities  of  steel. 


THE    MATERIALS    OF   DESIGN 


TABLE  IX. — BRINELL  HARDNESS  NUMBERS. 


Diam.  of 

Hardness  number 

Approx. 

Diam.  of 

Hardness  number 

Approx. 

impres- 
sion. 

for  the 
standard  load  of 

tensile 
strength. 

impres- 
sion. 

for  the 
standard  load  of 

tensile 
strength. 

Mms. 

3000  kilograms. 

Tons. 

Mms. 

3000  kilograms. 

Tons. 

2'6 

555 

130 

4*25 

201 

47'2 

27 

514 

no 

4"3 

197 

45'2 

275 

495 

106 

4'35 

I92 

43  '6 

2-8 

477 

102 

4  '4 

...             I87             -. 

42-2 

2-85 

46  1 

98 

4'45 

...             I83            ... 

41.2 

2-9 

444 

95 

4'5 

179 

40*2 

2*95 

429 

92 

4*55 

174 

39'5 

415 

89 

170 

38-8 

3'°5 

401 

86 

4*65 

I67             ... 

38-2 

...         388         ... 

84 

47 

...             I63            ... 

37-6 

3'T5 

375 

81-5 

475 

I59 

37 

3'2 

...        363        ... 

79 

...             I56            ... 

36-2 

3'25 

352 

77 

4-85 

152 

35'3 

3'3 

34i 

75 

4'9 

149 

347 

3'35 

331 

73'5 

4'95 

...             I46            ... 

34'2 

3'4 

321 

72 

5'° 

143 

337 

3  '45 

311 

70 

5-1 

137 

32-8 

3'5 

302 

68 

5'2 

131 

32 

3'55 

293 

67 

5'3 

126 

31-2 

...        285        ... 

65-5 

5*4 

121 

30*5 

3-65 

277 

64 

5*5 

116 

29-8 

37 

269 

62-5 

in 

29*2 

375 

262 

57 

107 

28-5 

255 

60 

103 

28-0 

3-85 

248 

59 

5'9 

99-2     ... 

27-4 

3*9 

241 

58 

6-0 

95*5     ••• 

26*9 

3'95 

235 

57 

6-1 

92 

26*4 

4-0 

229 

56 

6'2 

887     ... 

26*0 

4'°5 

223 

55 

6-3 

85-5     ... 

25'5 

217 

54 

6-4 

82-5     ... 

25 

4-15 

212 

53 

6-5 

79-6     ... 

24*6 

4-2 

2O7 

5° 

N.B. — With  the  aid  of  the  above  table  the  Brinell  Hardness  number 
and  approximate  tensile  strength  can  be  obtained  from  a  knowledge 
of  the  diameter  of  the  impression  formed  in  the  material. 

Factor  of  Safety. — The  relationships  between  the  elastic 
constants  are  obtained  from  the  Theory  of  Elasticity.  Theo- 
retical considerations  will  generally  produce  a  design,  but 
whether  such  a  design  is  practical  or  not  depends  upon  a 
large  number  of  varying  factors,  such  as  economy  and  facility 
in  production,  and  economy  in  upkeep.  In  most  cases  some 


24  AEROPLANE    DESIGN 

modification  from  the  theoretical  design  will  be  necessary, 
and  it  is  in  this  direction  that  experience  and  practice  tell. 
In  all  design  work  using  formulae,  and  more  especially  in  cases 
where  a  large  number  of  empirical  formulae  are  used,  it  is 
exceedingly  important,  if  these  formulae  are  to  be  used  intelli- 
gently, to  know  and  to  understand  the  fundamental  principles 
underlying  the  construction  of  such  formulae,  and  to  realise  and 
appreciate  the  various  assumptions  that  have  been  made  in 
arriving  at  any  particular  formula. 

To  allow  for  the  effect  of  these  assumptions  and  for 
accidental  overloads  that  may  occur  in  any  portion  of  the 
structure,  it  is  customary  to  design  structures  considerably 
stronger  than  an  investigation  shows  to  be  necessary.  This  allow- 
ance is  termed  the  Factor  of  Safety,  and  is  of  prime  importance 
in  aeronautical  practice  where  weight-saving  must  be  considered 
down  to  the  last  detail.  Too  high  a  factor  of  safety  leads  to  a 
heavy  structure,  while  too  small  a  factor  will  probably  result  in 
an  accident  in  mid-air.  From  theoretical  considerations  the 
ideal  design  would  be  that  design  in  which  such  a  factor  of 
safety  had  been  used  in  the  various  component  parts  that  each 
of  those  component  parts  would  be  on  the  point  of  failure  at 
the  same  moment.  Table  X.  gives  the  Factors  of  Safety  in 
general  use  to-day. 

TABLE  X. —  FACTORS  OF  SAFETY. 

Factor  of  Safety 

Type  of  Machine.  Factor  of  safety  in  terminal 

C.P.  forward.  nose  dive. 

Fast  Scout  or  Sporting  Machine  (that  is, 
a  machine  liable  to  be  stunted,  etc.)— 

Up  to  3,000  Ibs.    ...         ...         ...         8  ...         i "5 

3,000  to  io,ooolbs.          ...          ...         8-6* 

Over  10,000 Ibs.   ...         ...         ...         6  ...         1*5 

Commercial    Machines  (this  type  must 
not  be  stunted) — 

Up  to  5,000  Ibs 6  ...  '5 

5,000  to  io,ooolbs.          ...         ...  5  ...  '5 

10,000  to  30,000  Ibs.        ...          ...  5-4*  ...  33 

30,000  to  50,000  Ibs.       ...         ...  4  -  3*5*  ...  '25 

Over  50,000  Ibs.   ...         ...         ...  3*5  ...  '25 

*  Reduction  in  factor  proportional  to  increase  in  weight. 

Wind  Pressure. — A  large  amount  of  research  work  has 
been  carried  out  upon  the  subject  of  wind  pressures  during 
recent  years.  Anemometers,  for  example,  are  maintained  upon 
the  Tower  Bridge,  under  the  supervision  of  the  National  Physical 


THE    MATERIALS   OF   DESIGN 


Laboratory,  and  the  results  and  readings  obtained  are  published 
from  time  to  time.  Generally  speaking,  the  pressure  varies 
approximately  as  the  square  of  the  velocity.  Table  XL  gives 
in  a  convenient  form  an  idea  of  the  velocities  and  pressures  due 
to  various  types  of  winds. 


Velocity, 
m.p.h. 

4 
10 

I5 

20 

30 
40 

5o 
60 
70 
80 
90 

IOO 


Remarks. 


TABLE  XL — WIND  PRESSURES. 

Pressure, 
Ibs.  per  sq.  ft. 

•08        Light  breeze. 

•49        Fair  breeze. 

I'll        Strong  breeze. 

1*97        Very  strong  breeze. 

4-43        ...         ...  Brisk  gale. 

7-87        High  wind. 

12-30        Very  high  wind. 

1670        Storm  wind. 

2 2 '8 1  Great  storm. 


Hurricane. 


FIG.  7.— Variation  of  Pressure  and  Temperature  with 
Change  in  Altitude. 


26  AEROPLANE   DESIGN 

The  variation  of  pressure  of  the  atmosphere  at  varying 
heights  must  also  be  borne  in  mind,  not  only  in  connection  with 
its  effect  on  the  lifting  capacity  of  the  wings  of  a  machine,  but 
also  in  its  effect  upon  the  power  developed  by  the  engine. 

Fig.  7  illustrates  the  change  both  of  pressure  and  of  tem- 
perature with  varying  altitude. 

Stress  Diagrams. — The  preparation  of  stress  diagrams  for 
different  components  of  an  aeroplane  constitutes  a  very  large 
portion  of  the  routine  work  of  an  aircraft  designer,  the  draughts- 
man to  whom  this  duty  is  delegated  being  frequently  referred  to 
in  the  drawing-office  as  a  'stress  merchant'  The  authors  of 
this  work  have  frequently  found,  in  their  experience,  that  the 
average  draughtsman  has  but  little  conception  of  the  funda- 
mental principles  underlying  the  construction  of  stress  diagrams, 
so  that  he  is  quite  unable  to  tackle  a  diagram  for  a  case  that  is 
somewhat  unusual.  They  therefore  make  no  apology  for  dealing 
with  this  question  fully,  and  hope  that  their  explanations  will 
lead  to  a  clearer  conception  of  the  whole  matter. 

The  fundamental  theorem  in  connection  with  this  subject  is 
that  known  as  the  Triangle  of  Forces,  which  states  :  '  If  three 
forces,  acting  at  a  point,  be  represented  in  magnitude  and 
direction  by  the  sides  of  a  triangle  taken  in  order,  they  will  be 
in  equilibrium.'  It  should  be  noted  that  the  converse  of  this 
theorem  is  also  true,  namely,  '  If  three  forces,  acting  at  a  point, 
be  in  equilibrium,  they  can  be  represented  in  magnitude  and 
direction  by  the  sides  of  any  triangle  drawn  so  that  its  sides  are 
respectively  parallel  to  the  directions  of  the  forces.'  As  an 
extension  of  this  proposition  we  have  the  theorem  known  as  the 
Polygon  of  Forces,  which  states  :  *  If  any  number  of  forces 
acting  on  a  particle  can  be  represented  in  magnitude  and 
direction  by  the  sides  of  a  polygon  taken  in  order,  the  forces  are 
in  equilibrium.'  The  construction  of  stress  diagrams  is  based 
upon  this  theorem. 

For  equilibrium  it  will  be  noticed  that  the  triangle  or  the 
polygon  must  be  closed,  hence  the  stress  diagram  must  also 
close. 

The  formal  treatment  of  statical  problems  by  graphical 
methods  is  due  to  Clerk  Maxwell,  who  published  papers  'On 
Reciprocal  Figures  and  Diagrams  of  Forces'  in  1864,  and 
subsequent  years. 

Two  plane  rectilinear  figures  are  said  to  be  reciprocal  : 

I.  When  they  consist  of  an  equal  number  of  straight  lines  or 
edges,  such  that  corresponding  edges  are  parallel. 


THE    MATERIALS    OF  DESIGN  27 

2.  When  the  edges  which  meet  in  a  point  or  corner  of  either 
figure  correspond  to  lines  which  form  a  closed  polygon 
or  face  in  the  other  figure. 

It  will  be  observed  that  in  order  to  obtain  a  reciprocal  figure 
every  corner  must  have  at  least  three  edges  meeting  at  it,  and 
since  an  edge  can  have  only  two  ends,  each  of  which  represents 
a  face  in  the  other  figure,  two  faces  and  two  only  intersect  in 
each  edge. 

The  best  way  of  illustrating  the  fundamental  principles 
enunciated  above  is  by  means  of  a  concrete  example.  We  will 
take  as  a  first  illustration  the  simple  roof  truss  shown  in  Fig.  8. 


FIG.  8. — Frame  Diagram. 

It  must  be  remembered  in  drawing  stress  diagrams  that  the 
following  assumptions  are  made  when  the  principle  of  reciprocal 
figures  is  applied  to  any  framed  structure  : 

1.  That  the  members  (or  bars)  of  the  structure  are  rigid. 

2.  That  these  members  are  connected  together  by  means  of 

frictionless  pin-joints. 

3.  That  the  loads  act  at  these  pin-joints. 

The  first  two  assumptions  are  rarely  justified  in  English 
engineering  practice,  and  where  the  third  assumption  is  not 
fulfilled  it  is  customary,  for  the  purpose  of  drawing  the  stress 
diagram,  to  divide  up  the  load  and  place  a  portion  at  each  joint. 

In  drawing  a  stress  diagram  there  are  two  systems  of  forces 
to  be  considered,  namely,  the  external  forces  and  the  internal 
forces.  Thus  in  Fig.  8  the  external  forces  are  those  shown  by 
P  =  8  tons,  Q  —  4  tons,  R  =  5  tons,  and  by  drawing  the  stress 
diagram  we  determine  the  internal  forces  acting  in  the  members 
of  the  frame.  From  the  knowledge  thus  obtained  we  can  proceed 
to  the  detail  design  of  these  members.  The  internal  forces  act 
along  the  neutral  axes  of  the  members. 

The  frame  diagram  (F"ig.  8)  is  first  lettered  according  to 
Bow's  notation — that  is,  letters,  figures,  or  other  symbols  are 
placed  between  the  external  forces  acting  and  also  between  the 


28 


AEROPLANE    DESIGN 


members  of  the  frame.  The  force  P  is  now  termed  the  force  A  B, 
the  force  Q  is  the  force  B  c,  and  so  on.  The  object  of  this 
notation  will  be  apparent  on  the  completion  of  the  stress 
diagram.  Commencing  with  the  force  A  B,  we  set  down  the 
line  a  b  parallel  to  the  direction  of  the  force  A  B  and  representing 
to  some  suitable  scale  its  magnitude  (8  tons).  From  b  we  draw 
b  c  parallel  to  the  direction  of  the  force  B  C  to  represent  its 
magnitude  (4  tons)  to  the  same  scale  that  a  b  represents  the 
magnitude  of  A  B.  Joining  ca  gives  the  direction  and  magnitude 
of  the  force  C  A — namely,  5  tons.  The  triangle  (polygon)  of 
forces  for  the  external  loading  of  the  frame  under  consideration 
has  now  been  drawn.  Through  a  we  now  draw  a  line  parallel 
to  the  direction  of  the  member  A  D,  and  through  c  a  line  parallel 
to  the  direction  of  the  member  c  D.  These  lines  intersect  in  d, 
and  acd  is  the  polygon  of  forces  for  the  corner  where  the 


FIG.  9. — Stress  Diagram. 

force  R  acts.  Through  b  we  now  draw  a  line  (b  d)  parallel  to 
the  direction  of  the  member  B  D.  This  should  intersect  the 
line  c  d  in  dy  and  its  agreement  or  non-agreement  provides  a 
measure  of  the  accuracy  of  the  construction  of  the  stress 
diagram,  b  c  d  is  the  polygon  of  forces  for  the  corner  where 
the  force  Q  acts,  and  a  b  d  is  the  polygon  of  forces  for  the  corner 
where  the  force  P  acts. 

The  stress  diagram  can  now  be  scaled  for  the  forces  acting 
in  each  member,  and  the  advantage  of  Bow's  notation  is  at  once 
apparent,  since  the  line  a  d  (small  letters)  in  the  stress  diagram 
gives  the  force  acting  in  the  member  A  D  (large  letters)  ;  the  line 
b  d  in  the  stress  diagram  the  force  in  the  member  B  D  ;  and  the 
line  c  d  in  the  stress  diagram  the  force  in  the  member  C  D.  It  is 
next  necessary  to  determine  whether  the  members  of  the  frame 
are  in  compression  or  in  tension — that  is,  whether  they  are 
acting  as  struts  or  as  ties  ;  because  the  manner  of  their  subse- 
quent design  depends  upon  the  way  in  which  they  are  function- 


THE    MATERIALS    OF    DESIGN 


29 


ing.  The  easiest  way  of  determining  this  is  to  consider  the 
polygon  of  forces  for  each  corner  of  the  frame  separately,  con- 
sidering first  the  corner  where  the  force  P  acts.  The  polygon 
of  forces  is  given  by  the  triangle  a  b  d,  and  the  direction  of  the 
force  P  is  already  known.  Indicating  this  direction  by  an 
arrow-head  as  shown  in  Fig.  10  (a\  we  can  insert  arrows  upon 
the  remaining  sides  of  the  polygon,  because  we  know  from 
fundamental  principles  that  these  arrows  must  follow  round  the 
sides  of  the  polygon  in  order,  so  that  there  may  be  equilibrium. 


Fig  10 


Rg.ll 


(a) 


These  directions  can  now  be  transferred  to  the  frame  diagram, 
as  shown  in  Fig.  10  (b). 

When  an  arrow  so  transferred  points  towards  the  corner,  the 
member  it  belongs  to  is  in  compression  ;  while  if  it  points  away 
from  the  corner,  the  member  is  in  tension.  We  thus  see  that 
the  members  A  D  and  B  D  are  in  compression — that  is,  that  they 
must  be  designed  as  struts. 

Dealing  with  the  corner  where  the  force  Q  acts,  we  proceed 
in  exactly  the  same  manner,  bed,  Fig.  n  (n)  is  the  polygon  of 
forces,  and  the  direction  of  the  force  B  C  is  known,  whence  the 
remaining  directions  can  be  inserted.  These  directions  can  be 
transferred  to  the  frame  diagram,  Fig.  1 1  (£),  from  which  we 


30  AEROPLANE    DESIGN 

see  that  the  member  B  D  is  in  compression,  and  the  member  c  D 
is  in  tension.  As  will  be  observed,  the  result  obtained  for  the 
member  BD  (compression)  agrees  with  that  obtained  in  Fig.  10. 

We  have  now  determined  the  nature  of  the  stress  in  each  of 
the  members  of  the  frame,  but  by  way  of  a  check  we  will  deal 
with  the  remaining  corner.  The  polygon  of  forces  and  the  corner 
are  shown  in  Fig.  12  (a)  and  (b\  from  which  we  see  that  the 
member  A  D  is  in  compression,  agreeing  with  the  result  obtained 
in  Fig.  10 ;  and  the  member  C  D  is  in  tension,  agreeing  with  the 
result  obtained  in  Fig.  11. 

Struts  and  ties  are  distinguished  from  each  other  on  the 


FIG.  13. — Methods  of  indicating  Struts  and  Ties. 

frame  diagram  in  three  different  ways,  as  shown  in  Fig.  13  a,  bt 
and  c. 

(a)  By  the  use  of  arrows.     Remember  that,  as  pointed  out 

above,  an  arrow  pointing  towards  a  joint  indicates  com^ 
pression,  while  an  arrow  pointing  away  from  the  joint 
indicates  tension. 

(b)  By  thickening  the  compression  members  only. 


THE    MATERIALS    OF    DESIGN  31 

(V)  By  two  small  cross  lines  upon  the  compression  members, 
and  one  cross  line  upon  the  tension  members,  leaving 
those  members  in  which  there  is  no  stress  without  any 
mark  at  all. 

Having  completed  the  stress  diagram,  the  results  obtained 
should  be  exhibited  in  a  neat  table  upon  the  drawing.  This 
table  should  also  indicate  those  members  which  are  in  com- 
pression and  those  which  are  in  tension.  There  are  two  methods 
of  showing  this,  namely — 

1.  By  underlining  the  compression  members. 

2.  By  placing  a  negative  sign  before  the  compression  mem- 

bers, since  compression  tends  to  shorten  a  member ; 
and  by  placing  a  positive  sign  before  a  tension  member, 
since  tension  tends  to  lengthen  a  member. 

The  table  for  the  frame  under  consideration  will  then  appear 
in  one  of  the  two  forms  shown  below. 

TABLE  XII.— MEMBER  FORCE  TABLE  XIIL— MEMBER 

IN  TONS.  FORCE  IN  TONS. 

AD        1 1 -QO  AD       -  ii-oo 

BD        ~  BD       775 

CD        6-62  CD       +    6-62 

We  have  taken  a  fairly  general,  though  simple,  example 
by  way  of  illustration.  Probably  in  an  actual  example  the  load 
P  would  act  vertically,  in  which  case  the  reactions  Q  and  R 
would  be  vertical,  and  the  triangle  of  external  forces — a  b  c — 
would  become  a  straight  line. 

As  further  exemplification  of  the  fundamental  principles,  we 
will  next  consider  the  stress  diagram  for  a  framed  structure  such  as 
is  shown  in  Fig.  14,  since  the  method  of  treatment — with  varia- 
tions, of  course,  to  suit  particular  cases — is  applicable  to  many 
forms  of  structures,  including  the  wing-spars  of  aeroplanes,  arid 
the  fuselages  of  aeroplanes.  Such  a  structure  as  outlined  is, 
strictly  speaking,  statically  indeterminate,  as  it  is  a  redundant 
frame,  but  for  most  practical  purposes  it  can  be  treated  by 
regarding  it  as  made  up  of  two  perfect  frames,  the  loads  being 
equally  divided  between  the  two  frames ;  and  then  finding  the 
stress  for  each  of  these  frames  independently,  and  afterwards 
adding  together  algebraically  the  stresses  obtained  for  the  mem- 
bers common  to  both  frames. 

The  division  of  this  structure  into  two  perfect  frames  is  shown 
in  Figs.  15  and  16.  The  stress  diagram  for  the  frame  of  Fig.  15 


AEROPLANE   DESIGN 


Ftq    16 


FiQ.18 

q 


FIGS.  14  to  1 8. — Load,  Frame,  and  Stress  Diagrams. 

is  shown  in  Fig.  17  ;  and  that  for  Fig.  16  is  shown  in  Fig.  18. 
In  order  to  clear  up  any  doubtful  points,  we  will  go  through  the 
construction  briefly.  The  reactions  in  this  case  are  found  by 


THE    MATERIALS    OF    DESIGN  33 

taking  moments  about  either  support.    For  example,  the  reaction 
at  the  left-hand  support  is  given  by  — 

,  r        12  x  10  +  10  x  20  +  8  x  -?o 
Reaction  left  =  -  --  -  $- 


40 
=  14  cwt. 

The  reaction  for  the  right-hand  support  can  be  found  in  a 
similar  manner,  or,  since  the  total  load  for  Fig.  15  is  30  cwts., 
the  reaction  at  the  right-hand  support  can  be  found  by  sub- 
traction, thus  — 

Reaction  right  =  30  -  14  =  16  cwt 

This  practice  is  not  to  be  recommended,  however,  as  it  does 
not  afford  any  check  upon  the  accuracy  of  the  arithmetic  of  the 
first  calculation,  and  such  checks  should  always  be  introduced 
into  practical  calculations  wherever  possible.  Thus,  in  the 
present  case,  the  two  reactions  should  be  calculated  separately,  and 
then  added  together,  to  see  that  their  sum  is  equal  to  30  cwt. 

Having  calculated  the  reactions,  the  polygon  of  forces  for  the 
external  forces  —  that,  is  the  straight  line  abcdea  —  can  be  drawn 
to  some  suitable  scale.  af\s  then  drawn  parallel  to  A  F,  and  ef 
parallel  to  E  F.  The  intersection  of  these  two  straight  lines  gives 
the  point/,  b  g  is  next  drawn  parallel  to  B  G,  to  meet/^-  drawn 
parallel  to  F  G  in  g.  g  h  is  then  drawn  parallel  to  G  H,  to  meet 
eh  drawn  parallel  to  EH  in  h,  and  thus  half  the  diagram  is 
completed.  It  is  a  good  plan,  in  drawing  complicated  stress 
diagrams,  to  work  from  each  end  in  turn,  so  that  any  drawing 
error  is  not  continued  through  the  whole  of  the  stress  diagram. 
It  is  therefore  advisable  to  start  now  from  the  other  end  of  the 
frame  diagram,  so  that  the  amount  of  closing  error  —  if  any  —  may 
be  kept  as  small  as  possible.  Consequently,  draw  dm  parallel 
to  D  M  to  meet  e  m  drawn  parallel  to  E  M  in  m  ;  and  then  m  k, 
c  /£,  parallel  respectively  to  M  K,  c  K,  to  obtain  the  point  k.  The 
line  kj  on  the  stress  diagram  tests  the  accuracy  of  your  drawing, 
for  a  line  through  k  parallel  to  K  J  on  the  frame  diagram  should 
pass  through  the  point  //  already  obtained  on  the  stress  diagram. 
If  there  is  a  big  closing  error,  it  is  advisable  to  redraw  the  figure 
completely,  and  if  the  error  is  at  all  appreciable,  it  should  be 
traced  and  corrected.  The  greatest  trouble  in  drawing  stress 
diagrams  correctly  in  practice  occurs  where  it  is  necessary  to 
draw  long  lines  on  the  stress  diagram  parallel  to  very  short  lines 
on  the  frame  diagram.  For  important  work  it  is  desirable  in  such 
cases  to  calculate  the  inclination  of  such  lines  by  trigonometrical 
methods,  in  which  way  a  very  fruitful  source  of  error  may  be 
eliminated. 


34 


AEROPLANE    DESIGN 


In  an  aeroplane  the  wings  support  the  whole  weight  of  the 
machine.  They  support  both  their  own  weight  uniformly  dis- 
tributed over  their  length,  and  the  weight  of  the  other  components 


Fig.  21   Frame  Diagram 


Fig.22 
5tTess  Diagram 


of  the  aeroplane  concentrated  at  certain  points.  From  a  structural 
point  of  view  they  are  therefore  wide,  flat  beams  stretching  out 
on  each  side  of  the  fuselage.  To  realise  what  the  load  on  them 
really  means,  we  can  imagine  the  plane  turned  upside  down. 


THE   MATERIALS    OF   DESIGN  35 

Fig.  19  shows  an  aeroplane  in  its  normal  attitude,  the  wings 
A  B,  CD  being  loaded  uniformly  by  upward  wind  forces, 
indicated  by  small  arrows,  the  sum  of  these  wind  forces  being 
equal  to  the  total  weight  of  the  aeroplane  acting  downwards 
as  shown.  The  strains  and  stresses  in  the  wings  of  the  machine 
would  therefore  be  exactly  the  same  if  the  machine  were  turned 
upside  down  as  shown  in  Fig.  20,  suspended  from  the  centre 
of  gravity,  and  weights  placed  uniformly  along  the  wings  as 
indicated,  the  sum  total  of  these  weights  being  equal  to  the 
total  weight  of  the  machine  less  the  weight  of  the  wing 
structure.  In  many  circumstances  the  load  on  the  wings  will 
be  many  times  the  total  weight  of  the  machine,  as  for  example 
when  the  aeroplane  is  being  flattened  out  after  a  nose  dive  or 
in  stunting.  The  biplane  arrangement  is  essentially  stronger 
than  the  monoplane,  because  it  can  be  braced  together  until 
it  forms  a  structure  analogous  to  a  bridge.  The  wings  of  a 
biplane  can  therefore  be  regarded  exactly  as  a  compound  girder 
in  bridge  design.  The  panels  are  formed  between  the  upper 
and  lower  spars,  and  as  there  are  usually  two  sets  of  spars  to 
each  wing,  there  will  be  two  sets  of  panels — a  front  and  a  rear 
set.  Fig.  21  shows  a  front  view  of  one  half  of  the  machine 
depicted  in  Figs.  19  and  20,  one  set  of  wires  having  been 
removed  because  it  is  assumed  in  aeroplane  design  that  only 
one  set  of  wires  is  acting  at  any  given  instant.  This  figure 
shows  the  simplest  form  of  the  frame  of  the  machine  illustrated, 
and  in  Fig.  22  the  corresponding  stress  diagram  is  drawn.  The 
method  of  drawing  this  diagram  should  be  quite  obvious  from 
what  has  been  said  above  with  reference  to  such  diagrams. 
The  stress  diagram  for  the  other  half  of  the  machine  will  be 
exactly  similar  but  reversed  in  direction.  Further  examples 
of  the  application  of  stress  diagrams  to  the  design  of  the  wings 
will  be  given  in  Chapter  V. 

Method  of  Sections. — This  method,  which  is  also  known 
as  Ritter's  method,  or  method  of  moments,  generally  entails  much 
elaborate  calculation,  and  in  most  cases  the  ordinary  graphical 
method  of  obtaining  the  forces  acting  in  the  various  members  of 
a  structure  as  outlined  above  is  much  to  be  preferred.  In  some 
few  cases,  however,  the  method  of  moments  offers  advantages, 
and  the  results  obtained  are  of  course  more  accurate  than  those 
obtained  by  reciprocal  diagram  work.  On  this  account,  in  very 
important  design  work,  it  should  be  used  as  a  check  upon  the 
accuracy  of  the  graphical  construction  for  the  main  members. 
By  its  aid,  also,  points  of  difficulty  which  sometimes  arise  in 
complicated  frame  structures  can  be  overcome. 


36  AEROPLANE   DESIGN 

The  method  of  moments  will  be  illustrated  by  means  of  a 
worked  example,  as  the  writers  are  strongly  of  the  opinion  that 
'  Example  is  better  than  precept.' 

We  will  take  for  our  example  the  Warren  frame  of  30  feet 
span,  shown  in  Fig.  23.  It  has  five  equal  equilateral  bays  of 
6  feet  span,  and  is  loaded  at  the  lower  flange  with  loads  of  7,  5, 
and  2  cwt.  at  the  first,  second,  and  third  nodes  from  the  right- 
hand  support  as  shown. 


FIG.  23. — Method  of  Moments  of  Sections. 

It  may  be  noticed  in  passing  that  Bow's  notation    is    not 
convenient  for  the  method  of  moments. 
We  first  find  the  reactions  at  A  and  M. 
Taking  moments  about  M,  we  have 

RA  x  3°  =  2  x  18  +  5  x  12  +  7  x6 
whence  RA  =  4-6  cwt. 

and  RM  =  14  -  4'6  =  9*4  cwt. 

a  value  which  should  be  checked  by  taking  moments  about  A. 

Consider  the  right-hand  end  bay  J  K  M,  and  imagine  that  it 
is  cut  in  two  by  some  such  line  as  1-2,  then  the  moment  of  the 
forces  in  the  members  J  M,  J  K,  H  K  about  any  point  must  be 
equal  to  the  moment  of  the  external  forces  acting  either  to  the 
right  or  the  left  of  the  line  1-2  about  the  same  point,  for 
otherwise  the  structure  would  not  be  in  equilibrium.  Now,  if 
we  take  moments  about  the  point  K,  the  moment  of  the  forces 
in  the  members  J  K,  H  K  about  K  is  zero,  and  we  are  left  with 
the  moment  of  the  force  in  J  M  about  K,  equal  to  the  moment 
of  the  external  forces  to  the  right  or  left  of  1-2  about  K  ;  that 
is,  if  we  take  the  external  forces  to  the  right  of  the  line  1-2, 
we  have 

Force  in  j  M  x  K  N       =9-4x3 
or      Force  in  j  M  =  28'2/$'i<)6  =  5-43  cwts.  (Tension) 


THE    MATERIALS   OF   DESIGN  37 

Again  with  the  same  cutting  line,  taking  moments  about  J, 

Force  in  H  K  x  5*196  =     9-4x6 
or     Force  in  H  K  =  10*85  cwt.  (Compression) 

Again  with  the  same  cutting  line,  taking  moments  about  M, 

Force  in  j  K  x  5*196  =  Force  in  H  K  x  5*196 
or     Force  in  j  K  =  Force  in  H  K  =  10*85  cwt-  (Tension) 

It  will  be  noticed  of  course  that  for  equilibrium  here  the 
force  in  j  K  must  be  of  opposite  sign  to  the  force  in  H  K,  and 
since  H  K  is  in  compression,  J  K  must  be  in  tension. 

Next  take  a  cutting  line  such  as  3-4,  and  take  moments 
about  J,  then 

Force  in  K  M  x  5*196  =  9-4  x  6 
or      Force  in  K  M  =10*85  cwt.  and  is  in  compression. 

Again,  with  a  cutting  line  such  as  5-6,  taking  moments  about  G, 
we  have 

Force  in  H  j  x  5*196   =  9*4  x  12  -  7  x  6  -force  in  HK  x  5*196 

or     Force  in  H  j  =  13*6  -  10-85 

=     2 -7  5  cwt. 

With  the  same  cutting  line,  taking  moments  about  H, 

Force  in  GJ  x  5*196    =94x9-7x3 
or     Force  in  G  j  =  12*23  cwt. 

In  this  manner,  by  taking  fresh  cutting  lines  along  the 
girder  and  proceeding  bay  by  bay,  the  whole  of  the  forces  in 
the  various  members  can  be  evaluated.  Of  course  it  will  be 
easier,  when  half-way  along  the  girder,  to  commence  from  the 
left-hand  end  and  work  from  that  end  towards  the  centre,  just 
as  in  the  case  of  stress  diagrams  it  is  best  to  work  from  each  end. 


CHAPTER   III. 

THE  PROPERTIES  OF  AEROFOILS. 

Wind  Tunnel  Investigation. — In  dealing  with  the  subject 
of  the  aerofoil,  it  will  be  useful  to  commence  by  considering 
the  method  whereby  most  of  our  information  concerning  the 
characteristics  of  different  aerofoils  is  obtained,  namely,  the 
wind  tunnel  method.  By  the  use  of  the  wind  tunnel  (or  wind 
channel,  as  it  is  also  called)  it  is  possible  to  obtain  both  simply 
and  accurately  the  particular  qualities  of  various  wing  sections, 
and  then  by  a  comparison  of  their  relative  merits  to  deduce  the 
one  most  likely  to  give  the  desired  results  upon  a  particular 
machine.  Moreover,  this  method  enables  the  effect  upon  aero- 
dynamic characteristics  of  an  alteration  in  the  camber  or  shape 
of  an  aerofoil  to  be  observed,  and  by  its  assistance  the  most 
efficient  wing  section  for  various  specific  duties  can  be  evolved. 
-  To  carry  out  such  experiments  upon  a  full-sized  machine  is 
practically  impossible,  besides  being  extremely  dangerous  and 
very  expensive. 

It  will  be  appreciated  that  the  application  to  a  full-size 
wing  section  of  the  results  obtained  in  a  wind  tunnel  upon  a 
small-scale  model  must  necessarily  be  a  problem  of  considerable 
difficulty,  and  this  emphasises  the  importance  of  extreme 
accuracy  in  the  measurement  of  the  forces  upon  the  model  ;  for 
any  slight  error  involved  at  this  stage  will  naturally  be  greatly 
magnified  when  applied  to  full-scale  machines.  The  question 
of  scale  effect  has  been  the  subject  of  close  investigation,  the 
results  of  which  will  be  summarised  at  a  later  stage  in  this 
chapter. 

The  major  portion  of  our  knowledge  of  aerofoil  charac- 
teristics is  due  to  the  splendid  work  of  the  National  Physical 
Laboratory  at  Teddington,  and  to  the  work  of  Monsieur 
G.  Eiffel  in  his  laboratories  at  Auteuil,  near  Paris,  so  that  a 
brief  description  of  these  two  laboratories  should  suffice  for  a 
good  understanding  of  the  principles  underlying  the  construction 
and  use  of  wind  tunnels.  It  may  be  remarked  that  there  are 
also  excellent  aeronautical  laboratories  in  the  leading  European 
countries  and  in  the  United  States  of  America. 

The  N.P.L.  Four-foot  Tunnel.*— There  are  several  wind 
tunnels   at  the  N.P.L.,  including  two  of  7   feet  diameter,  but 
*  N.P.L.  Report,  1912-1913. 


THE    PROPERTIES    OF  AEROFOILS  41 

from  a  room  which  is  60  feet  long,  50  feet  wide,  and  with  an 
average  height  of  20  feet.  The  air,  after  entering  the  mouth  of 
the  tunnel,  passes  through  a  honeycomb,  which  can  be  seen  in 
the  half-section  on  EF,  Fig.  24,  and  then  along  the  main  trunk 
portion,  AA.  This  current  of  air  is  produced  by  the  airscrew  B 
(Fig.  24),  this  airscrew  being  driven  by  an  electric  motor 
through  the  line  of  shafting  shown  in  the  sectional  plan  (Fig.  24). 
Passing  through  the  airscrew,  the  wind  stream  enters  the 
specially  perforated  chamber,  CC,  and  is  squeezed  through  the 
walls  of  this  chamber  into  the  room  again  at  a  greatly  reduced 
velocity.  The  airscrew  has  a  pitch  of  2  feet,  and  is  made  up 
of  4  blades  of  a  constant  width  of  6  inches,  the  section  being 
that  of  a  previously  tested  aerofoil,  and  the  pitch  being  calcu- 
lated from  the  angle  of  no  lift.  It  is  possible  to  vary  con- 
tinuously the  speed  of  the  air  stream  through  the  working  portion 
from  10  to  50  feet  per  second.  At  the  highest  speed  the  airscrew 
is  making  1350  r.p.m.,  and  absorbs  about  8  h.p.,  20%  of  this 
amount  being  lost  in  frictional  resistance  at  the  honeycomb. 
The  wind  velocity  is  measured  by  means  of  a  Pitot  tube,  which 
is  illustrated  and  fully  described  in  Chapter  XII.  As  a  rough 
check  upon  this  speed  a  recording  speedometer  is  attached  to 
the  motor  shafting. 

It  is  very  essential  that  the  distribution  of  velocity  over  the 
central  portion  of  the  working  part  of  the  tunnel  should  be 
uniform.  An  investigation  was  made  into  this  question  by 
means  of  two  anemometers,  one  of  which  was  fixed  and  used  as 
a  standard  of  reference,  while  the  other  was  moved  from  point  to 
point  in  the  cross-section.  It  was  found  that  over  a  central 
square  of  2*5  feet  side,  the  velocity  measurements  did  not  differ 
more  than  i°/Q  from  the  mean. 

The  Balance. — This  balance  has  been  designed  for  use 
under  the  most  complex  conditions,  including  investigations 
into  the  stability  of  a  complete  model.  The  arm  of  the  balance 
which  carries  the  model  under  test  projects  through  the 
bottom  of  the  channel.  This  arm  is  covered  by  a  wind  shield 
shaped  like  a  low-resistance  strut,  and  the  hole  where  the  arm 
passes  through  the  floor  of  the  tunnel  is  closed  by  means  of  an 
oil  seal.  Unless  sealed,  the  gap  between  the  balance  and  the 
arm  and  its  shield  would  allow  air  at  high  velocity  to  enter  the 
tunnel  in  the  neighbourhood  of  the  model,  owing  to  the  static 
pressure  in  the  tunnel  being  less  than  the  atmospheric  pressure 
in  the  room  outside.  The  use  of  a  spindle  to  support  the  model 
introduces  measurable  disturbances  in  its  own  plane  for  some 
distance  downwind,  and  corrections  have  to  be  applied.  The 


AEROPLANE    DESIGN 


balance  is  therefore  arranged  in  such  a  way  that  any  required 
measurement  can  be  obtained  without  changing  the  spindle  or 
its  position  relative  to  the  model,  so  that  any  corrections  which 
have  to  be  made  for  the  influence  of  the  spindle  on  the  air  flow 
can  be  deduced  from  a  second  experiment  on  the  same  model, 
when  held  by  the  spindle  in  a  different  manner. 


FIG.  27. 

A  photographic  view  of  the  balance  is  shown  in  Fig.  27,  and 
an  elevation  of  the  balance  is  shown  in  Fig.  28.  The  arrange- 
ments of  this  balance  allow  for  measurement  of  forces  along, 
and  moments  about,  three  fixed  rectangular  axes.  The  main 
part  of  the  balance  consists  of  three  arms  mutually  at  right 


i 


S  -    Oil  Se.l    to    frtrent-    ,oru«fc     of  »ir 

Arowgfc    floor  of     Vum*! 

FF  -    VfcigWa    for    J.relmi«ary  adjurf"*"''   of 
balance    fwior   to  m»W"»g  a  *»*  wtx^J 
a    model 
B     -    Slid.ng    weioM   idjurfmmt  /or  «-.#««.* 

B««      of      f«sV       module 
C     '     Divided      circle    (or  adjusting    me 

mclMV*.ot7     of  «««  model      fe    ««    «'' 

*r«^      C*l  W  rearf     to    O  C    ly   ver- 

0  fW    of    eue>>eneion    of   tolanet    for 

-    of    UfV    ««d    Drag.     RbW.o* 

a«i«  J>rev»*c(     ty    «a« 
Ce<*«  Jwirf    usW   m    cooju^chot?    »*  O    f 


FIG.  28.— N.P.L.  Aerodynamical  Balance. 


44  AEROPLANE    DESIGN 

angles,  each  arm  being  counterbalanced.  The  centre  lines  of 
these  arms  meet  in  a  point  at  which  a  steel  centre  is  fixed. 
The  weight  of  the  balance  is  taken  on  this  point,  which  rests  in 
a  hollow  cone  in  a  column  fixed  to  the  floor  of  the  room. 
Three  degrees  of  freedom  are  thus  allowed,  permitting  measure- 
ments to  be  made  of  the  moments  about  the  centre  lines  of  the 
three  arms,  which  constitute  a  system  of  rectangular  axes  of 
reference.  The  vertical  arm  of  the  balance  passes  through  the 
floor  of  the  tunnel  and  supports  the  model  under  test.  It  can 
be  rotated  from  the  outside  of  the  tunnel,  and  this  rotation 
provides  one  of  the  two  angle  settings  which  have  been  shown 
to  be  necessary  for  general  work.  The  two  horizontal  arms  are 
set  along  and  at  right  angles  to  the  wind  direction,  and  are 
used  for  determinations  of  lift  and  drag,  or  lateral  force  and 
drag,  as  may  be  required.  The  forces  on  the  model  are  counter- 
balanced by  dead  weights  hung  from  the  ends  of  the  horizontal 
arms,  fine  adjustment  being  provided  by  the  movement  of  a 
jockey  weight  along  the  arm.  The  rotation  of  the  balance 
about  the  vertical  axis  is  prevented  by  a  torsion  wire,  the  twist 
in  which  is  measured  on  a  torsion  head,  and  thus  the  moment 
about  a  vertical  axis  is  determined. 

The  force  along  the  vertical  axis  is  measured  on  a  horizontal 
weighing  lever,  the  force  on  the  model  being  transmitted  to  the 
lever  through  a  vertical  rod  which  slides  freely  inside  the 
vertical  arm  of  the  balance.  Two  moments  are  also  measured 
on  this  latter  weighing  lever.  The  model  is  held  to  the  vertical 
balance  arm  by  a  special  attachment,  which  allows  rotation  to 
occur  about  a  horizontal  axis  in  any  desired  direction,  this  axis 
being  much  nearer  to  the  model  than  the  axis  of  rotation  of  the 
main  balance  arms.  The  rotation  of  this  special  attachment  is 
controlled  by  connecting  it  by  a  short  arm  to  the  top  of  the 
vertical  sliding-rod.  The  immediate  attachment  to  the  model 
allows  an  alteration  of  angle  to  be  made  about  a  horizontal  axis, 
which  is  fixed  relative  to  the  model.  This  adjustment  can  only 
be  made  from  inside  the  tunnel. 

Of  the  six  force  and  couple  measurements  necessary  for  the 
examination  of  an  unsymmetrically  situated  model,  it  is  possible 
to  make  four  simultaneously.  Except  in  special  circumstances, 
however,  it  is  not  desirable  to  make  so  many  observations  at  the 
same  time,  and  locking  arrangements  are  therefore  provided  to 
reduce  the  number  of  degrees  of  freedom.  A  simple  locking 
device  also  holds  the  balance  from  movement  in  any  direction 
when  not  in  use. 

Rapid  oscillations  are  damped  out  by  means  of  dash-pots. 
On  the  lower  part  of  the  vertical  arm,  weights  can  be  attached 


THE    PROPERTIES    OF   AEROFOILS  45 

which  allow  changes  to  be  made  in  the  sensitivity  of  the  balance, 
so  that  models  of  greatly  varying  size  can  be  readily  tested. 

LIFT  AND  DRAG  MEASUREMENTS. — For  this  purpose  the 
balance  is  supported  at  the  point  O  only,  and  a  locking  device 
prevents  rotation  about  a  vertical  axis.  The  balance  is  then 
free  to  rotate  about  two  horizontal  axes  only. 

VERTICAL  FORCE  MEASUREMENT. — The  vertical  rod  in  the 
upper  portion  of  the  balance  is  guided  by  four  rollers,  so  that  it 
can  slide  in  a  vertical  direction  but  not  twist.  The  rod  will 
move  along  its  axis  under  a  force  of  O'oooi  Ib. 

COUPLE  ABOUT  A  VERTICAL  Axis. — For  this  purpose  the 
centre  H  is  held  in  a  conical  cup  by  the  spring  K,  which  is  not 
sufficiently  powerful  to  lift  the  upper  centre  O  off  its  seating. 
The  couples  are  therefore  measured  about  an  axis  through  O 
and  II,  and  special  precautions  have  been  taken  in  the  balance 
to  ensure  that  the  axis  OH  is  in  the  vertical  position.  The 
rotation  about  this  axis  is  controlled  by  the  torsion  wire  T,  the 
twist  being  measured  on  the  torsion  head  TH  by  the  amount  of 
rotation  necessary  to  bring  a  crosswire  attached  to  the  balance 
into  alignment  with  a  crosswire  in  the  microscope  M,  which  is 
fixed  to  the  balance  support. 

MEASUREMENT  OF  DRAG  ALONE. — For  this  purpose  the 
support  for  the  centre  O  is  lowered  until  the  balance  rests  on 
two  points  on  either  side,  the  centre  point  then  being  out  of  use. 
This  measurement  is  used  in  those  cases  where  there  is  no 
appreciable  lift. 

The  Eiffel  Laboratory.* — Eiffel's  early  wind-channel  ex- 
periments were  conducted  in  a  laboratory  erected  in  the  Champ  de 
Mars  at  Paris.  These  experiments  were  carried  out  to  determine 
the  force  exerted  upon  a  flat  plate,  and  were  made  in  conjunction 
with  the  method  of  dropping  flat  plates  from  the  Eiffel  Tower 
in  Paris  for  a  similar  purpose.  Much  useful  work  was  carried 
out  in  this  early  tunnel,  but  in  order  to  be  able  to  experiment  at 
speeds  more  nearly  approaching  those  of  an  aeroplane  in  flight 
there  was  built  at  Auteuil  in  1912  a  new  laboratory  and  wind 
tunnel,  of  which  illustrations  are  shown  in  Figs.  29-33. 

The  experimental  chamber  (see  Figs.  30  and  32)  is  an  air- 
tight room.  Leading  to  this  room  are  a  pair  of  funnel-shaped 
collectors  (see  Fig.  31,  p.  40)  through  which  the  air  is  drawn  from 
the  hangar  outside  (see  Fig.  30,  p.  46).  In  the  new  channel  the 

*  From  information  communicated  bv  Mons.  G.  Eiffel. 


46 


AEROPLANE   DESIGN 


outer  and  inner  diameters  of  the  larger  collector  are  13  feet  and 
6J  feet  respectively,  and  it  is  1 1  feet  in  length.  The  effect  of  so 
reducing  the  cross-sectional  area  is  to  raise  the  velocity  of  the 


t  FIG.  29. — Sectional  Elevation  of  Wind  Tunnel  in 

Eiffel  Aerodynamical  Laboratory. 

air  stream  and  diminish  its  pressure  correspondingly.  Conse- 
quently the  model  is  under  investigation  in  a  region  of  high 
velocity  and  low  pressure  (see  Fig.  33).  By  measuring  the 


FIG.  30. — Sectional  Plan  of  Wind  Channel  in 
Eiffel  Aerodynamical  Laboratory. 

difference  in  pressure  between  the  experimental  chamber  and  the 
air  in  the  hangar  outside,  the  velocity  of  the  air  stream  can  be 
deduced  from  the  formula 

#2_  2gh         Formula  10 

where  h  is  the  difference  in  pressure  observed.  Massing  across 
the  experimental  chamber  the  air  stream  enters  the  discharger, 
which  is  an  expanding  chamber  30  feet  long,  leading  to  the  air- 
screw. This  airscrew  is  actuated  by  a  50  h.p.  electric  motor. 
This  discharger  serves  to  lower  the  velocity  and  raise  the 
pressure  of  the  air  stream,  thus  reducing  the  power  required 


THE    PROPERTIES    OF   AEROFOILS  47 

to  drive  the  airscrew  and  returning  the  air  to  the  hangar 
without  setting  up  pulsations.  A  maximum  speed  of  TOO  feet 
per  second  can  be  attained  in  the  experimental  chamber.  The 
observers  are  situated  on  a  platform  above  the  air  stream  and 
model  as  shown  in  Fig.  32,  a  position  which  is  very  convenient 
for  experimental  purposes. 

The  investigations  carried  out  by  Eiffel  include  the  deter- 
mination of  forces  and  moments  upon  flat  plates  and  aerofoils, 
the  resistances  of  wing  structures,  scale  model  tests,  the  appli- 
cation of  results  to  full-sized  machines,  and  the  performance 
of  model  airscrews. 

The  Flat  Plate. — The  force  exerted  upon  a  flat  plate 
suspended  normally  to  a  current  of  air  is  at  the  basis  of  ex- 
perimental aeronautics.  A  very  thorough  investigation  of  this 
fundamental  problem  was  carried  out  by  Dr.  Stanton  at  the 
N.P.L.  As  a  result  he  found  that  the  force  (F)  varied  directly 
as  the  area  of  the  plate  (A),  the  square  of  the  velocity  of  the 
plate  relative  to  the  wind  (V),  and  that  the  relationship  could  be 
expressed  by  means  of  the  formula 

F  =  K  £  AV2 Formula  n 

g 

where  K  is  a  coefficient  depending  upon  the  units  used  and  the 
size  of  the  plate  under  investigation. 

From  Formula  1 1  we  see  that  the  pressure  per  unit  area 

=  ~  =  K^V2  .  Formula  n  (a) 

.  A  S 

These  relationships  are  independent  of  the  system  of  units  used  ; 
if  the  units  are  the  foot,  pound,  and  second,  the  value  of  K 
increases  from  O'52  for  a  plate  2  inches  square  to  a  value  of  0*62 
for  plates  between  5  and  10  feet  square. 

Eiffel  obtained  very  similar  results  at  his  laboratory,  and 
enlarged  the  scope  of  the  investigation  to  include  plates  of 
varying  aspect  ratio,  that  is,  ratio  of  span  to  chord.  He  found 
that  the  effect  of  increasing  the  span  relative  to  the  chord  was 
to  increase  the  normal  pressure  on  the  plate.  His  results  are 
embodied  in  Table  XIV. 

TABLE  XIV. — INFLUENCE  OF  ASPECT  RATIO  ON  THE  NORMAL 
PRESSURE  OF  A  FLAT  PLATE.     (EIFFEL.) 

Aspect  ratio      ...       11-53        6        10      14-6    20    30     41-5    50 
Ratio  of  pressures 
Rectangle 
Square  I'°°  r°4  I>07  ri°  I§145   T'25  I>34  *'4  I>435  I>47> 


48  AEROPLANE    DESIGN 

It  will  be  seen  from  the  above  table  that  the  normal  pressure 
on  a  plate  of  aspect  ratio  6  is  10%,  and  of  aspect  ratio  14-6  is 
2 5%  greater  than  that  on  a  square  plate  of  the  same  area  at  the 
same  speed.  This  effect  is  due  to  the  lateral  escape  of  the  air 
towards  the  ends  of  the  plate,  and  will  be  more  fully  considered 
in  relation  to  aerofoil  sections. 

The  Inclined  Flat  Plate. — The  next  step  was  to  investigate 
the  effect  of  inclining  the  plate  to  the  direction  of  the  air  stream, 
and  this  was  undertaken  both  by  the  American  experimenter, 


20° 


30°  -fO*  50°  60° 

Angle    of    hade  nee   O 


do" 


90° 


FIG.  34. — Effect  of  Aspect  Ratio  upon  Pressure 
on  Inclined  Plane. 

Langley,  and  Eiffel,  from  the  latter  of  whom  most  of  our  infor- 
mation on  this  problem  is  derived.  It  was  found  that  for  small 
angles  of  incidence  of  the  plate  to  the  direction  of  the  air  stream 
the  resultant  force  on  the  plate  is  given  by  the  expression  :  • 

Force  =   F  =  C  ^  A  V2  8    Formula  12 


and  the  pressure  per  unit  area  : 
=  A  =  C| 


Formula  12  (a) 


Reproduced  by  courtesy  oj  M.  Eiffel, 

FIG.  32. — Experimental  Chamber  in  Eiffel  Laboratory. 


Reproduced  by  courtesy  ofM.  Eiffel. 

FIG.  33. — Model  under  Test  in  Eiffel  Laboratory. 

Facing  fage  48. 


THE    PROPERTIES    OF   AEROFOILS 


49 


— that  is,  in  this  case  the  force  is  proportional  to  the  angle  of 
incidence  0  of  the  plate. 

As  the  angle  of  the  plate  relative  to  the  air  stream  increases, 
Formula  12  ceases  to  hold  good,  and  the  force  tends  towards 
the  value  given  by  Formula  n.  Fig.  34  shows  that  the  pressure 
on  a  square  plate  between  the  angles  of  25°  and  90°  is  greater 
than  that  at  90° — that  is,  when  the  plate  is  normal  to  the  wind 
direction.  The  effect  of  aspect  ratio  upon  an  inclined  flat  plate 
is  very  clearly  exhibited  by  the  graphs  shown  in  Fig.  34.  The 
series  of  curves  there  drawn  are  due  to  results  obtained  by  Eiffel, 
and  give  the  ratio  between  the  pressure  at  any  angle  6  and  the 
normal  pressure,  for  all  angles  from  o°  to  90°.  It  will  be  seen 
that  increase  of  aspect  ratio  produces  a  smaller  maximum 
normal  pressure,  but  that  for  small  angles  of  incidence  the 
normal  pressure  is  greatest  for  the  largest  aspect  ratio. 

The  resultant  force  (F)   on   an  inclined   flat   plate   can  be 


FIG.  35. 

resolved  into  two  particular  components  of  great  use  in  aero- 
nautical problems.  The  first  of  these  components  is  that  per- 
pendicular to  the  direction  of  the  air  stream,  and  is  known  as 
the  Lift ;  while  the  second  is  the  component  in  the  direction  of 
the  air  stream,  and  is  known  as  the  Drag.  These  components 
are  illustrated  in  Fig.  35. 

It  is  customary  to  express  these  components  in  the  manner 
shown  by  the  relationships  in  Formulae  13  and  14. 

Lift     =  Ky^AV2     Formula  13 

o 

Drag  =  KX^AV2     Formula  14 

o 

where  Ky  and  Kx>  known  as  the  Lift  and  Drag  absolute  co- 

E 


50  AEROPLANE    DESIGN 

efficients  respectively,  are  dependent  upon  the  angle  of  incidence. 
Formulae  13  and  14  may  be  regarded  as  the  two  fundamental 

r                                                        LIFT   . 
equations  of  aerodynamics,  and  the  ratio  is  a  measure  of 

the  efficiency  of  the  surface  under  test.  The  determination  of 
the  Lift  and  Drag  coefficients  for  surfaces  of  various  shapes 
is  a  function  that  has  been  admirably  performed  by  the  wind 
tunnel. 

Flat  Plate  moving  Edgewise. — The  investigation  of  the 
forces  in  this  case  was  carried  out  by  Zahm,  who  expressed  the 
results  obtained  in  the  relationship — 

F  =  K  A-93  V1'86  Formula  15 

We  shall  consider  this  question  further  when  dealing  with  the 
subject  of  skin  friction. 

These  fundamental  data,  while  not  directly  applicable  to 
practical  aeronautical  design  work,  provide  an  essential  founda- 
tion for  reference  in  the  ever-growing  field  of  aeronautical 
knowledge,  and  enable  the  true  significance  of  the  co-efficients 
for  objects  of  special  shapes,  such  as  aerofoils  and  stream-line 
sections,  to  be  more  fully  understood. 

The  Aerofoil. — Lilienthal  was  one  of  the  first  to  investigate 
by  means  of  scale  models  the  properties  of  the  cambered  aero- 
foil, and  to  point  out  its  much  superior  efficiency  over  that  of 
the  flat  plate. 

To-day,  the  analysis  of  a  wing  section  enables  the  values  of 
the  lift  and  drag  coefficients  to  be  determined  'over  a  large 
range  of  angles  and  also  provides  information  concerning  the 
pressure  distribution  over  the  upper  and  lower  surfaces. 

These  results  are  obtained  from  experiments  carried  out 
in  wind  tunnels  upon  carefully  prepared  scale  models.  The 
extreme  accuracy  with  which  the  forces  can  be  measured  and 
the  conditions  of  flight  approximated,  make  wind-tunnel  experi- 
ments of  increasing  importance  and  value.  To-day,  when  a 
new  type  oft  machine  is  being  designed,  an  accurate  model  is 
made  and  tested,  and  from  the  results  information  may  be 
gathered  leading  to  an  increased  efficiency  in  design. 

From  the  point  of  view  of  aeroplane  design,  the  determina- 
tion of  the  lift  and  drag  of  an  aerofoil  for  various  angles  of 
incidence  is  the  most  important  measurement  required,  and  it 
will  therefore  be  useful  to  consider  briefly  the  most  general 
method  of  recording  these  characteristics  of  an  aerofoil  and 


THE    PROPERTIES   OF   AEROFOILS  51 

their  common  features.  Table  XV.  gives  the  results  of  tests  in 
the  wind  tunnel  made  at  the  N.P.L.  upon  an  aerofoil  section 
known  as  the  R'.A.F.  6.  It  will  be  noted  that  the  lift,  drag,  and 
Lift/Drag  coefficients  are  given  in  absolute  units.  This  is  the 
method  now  adopted  in  England  in  giving  the  results  of  tests 
upon  modern  aerofoils,  and  expresses  the  values  of  Ky  and  Kx  in 
Formulae  13  and  14. 


Lift/Drag. 

4*5 
10*9 
14-3 
14*1 
12*9 

J1'4 
10*4 
9-3 

6'9 
4*1 

3*0 

2*6 

2*3 

The  curves  obtained  from  the  above  results  are  shown 
plotted  in  Figs.  36,  37,  and  38,  and  may  be  regarded  as  typical 
of  the  curves  obtained  from  tests  upon  model  aerofoils  possessing 
no  freak  characteristics. 

It  will  be  observed  that  the  point  of  no  lift  occurs  at  a  small 
negative  angle  of  incidence  :  that  is?  when  the  leading  edge  of 
the  aerofoil  is  inclined  downwards  to  the  direction  of  the  wind 
stream.  The  actual  value  of  the  point  of  no  lift  is  of  importance 
when  considering  questions  of  stability  and  control.  The  slope 
of  the  lift  curve  remains  practically  constant  up  to  a  point  shown 
by  c  in  Fig.  36,  and  is  of  importance  in  considering  stability. 
The  angle  of  incidence  corresponding  to  this  point  is  known  as 
the  critical  angle.  The  value  of  the  lift  corresponding  to  the 
maximum  Lift/Drag  ratio  is  indicated  by  the  point  B  (Figs.  38 
and  36).  The  angle  of  incidence  corresponding  to  this  point 
will  approximate  very  closely  to  that  chosen  for  the  most 
efficient  flying  position.  Moreover,  the  value  of  the  lift  at  this 
point  should  be  high  in  order  that  the  area  of  the  planes  may 
not  be  excessive.  On  the  other  hand,  it  should  not  approach 
the  point  of  maximum  lift  C  too  closely,  or  there  will  be  in- 


TABLE  XV.—  R.A.F. 

6  COEFFICIENTS. 

Angle  of 

Lift  coefficient 

Drag  coefficient 

incidence. 

absolute. 

absolute. 

-      2 

0*003 

O*02OI 

0 

0-074 

0*0165 

2 

0*173 

0*0159 

4 

0*275 

0*0193 

6 

0-354 

0*0252 

8 

0*423 

0*0329 

10 

0*496 

0*0433 

12 

0*564 

0*0545 

14 

o*593 

0*0640 

16 

0-605 

0*0875 

18 

°'55° 

0*1336 

20 

0*500 

0*1665 

22 

0*476 

0*1845 

24 

0*456 

0*2015 

52  AEROPLANE    DESIGN 

sufficient  latitude  for   manoeuvring.      Upon   the   value   of  the 
critical  angle  depends  the  landing  speed  of  the  machine ;  and  for 


16'  30'  24* 


of    INCIDENCE 


FIG.  36.  —  Lift  Curve. 


7 


8- 

OF      INCIDENCE 


FIG.  37.  —  Drag  Curve. 

a  given    wing  area  the  aerofoil  having  the   maximum  lift  co- 
efficient will  give  the  slowest  landing  speed.     The  critical  angle 


THE    PROPERTIES   OF   AEROFOILS 


53 


is  influenced  greatly  by  the  shape  of  the  aerofoil  and  slightly  by 
the  aspect  ratio.  . 


«     e 

IT 


-2*        0* 


16*  30' 


ANGUE     OF     INCIDENCC 


FIG.  38. — Typical  Lift/Drag  Curve  for  Aerofoil  Section. 


I 


T  e- 

Angle      of     Incidence 


FIG.  39. — Variation  of  Lift/ Drag  Ratio  with  Increase  of  Speed. 

After  passing  the  critical  angle,  the  lift  diminishes  sometimes 
slowly    and   sometimes   rapidly,   there   being   a    corresponding 


54 


AEROPLANE    DESIGN 


increase  in  the  drag.  When  testing  model  aerofoils  at  low 
speeds  there  is  occasionally  a  rapid  drop  in  the  lift  just  after 
the  critical  angle,  and  then  a  second  rise  in  the  value  of  the  lift 


Profile,    of  R.AF6 


o° 


8°  12° 

ANGLE         OF     INOOENCE. 


16° 


FIG.  40. — Typical  Curves  for  an  Aerofoil  Section. 
Combination  of  Figs.  36,  37,  38. 

coefficient  to  approximately  the  same  value  as  that  at  first 
obtained.  On  increasing  the  speed  of  the  air  current,  however, 
this  temporary  depression  disappears. 


THE    PROPERTIES    OF   AEROFOILS  55 

Fig.  37  shows  the  drag  curve,  from  which  it  will  be  seen  that 
the  drag  diminishes  to  a  minimum  value  between  o°  and  2°,  and 
that  it  remains  fairly  constant  in  this  neighbourhood,  and  then 
follows  approximately  a  parabolic  law  up  to  the  critical  angle, 
after  passing  which  point  there  is  a  very  rapid  increase. 

Fig.  38  shows  the  Lift/Drag  curve  for  the  aerofoil  whose 
curves  of  lift  and  drag  are  given  in  Figs.  36  and  37,  and  is 
plotted  from  the  calculated  results  shown  in  Table  XV. 

Fig.  39  shows  the  effect  upon  the  Lift/Drag  curve  of  increasing 
the  speed  of  the  air  current  in  the  wind  tunnel  for  the  same 
aerofoil. 

For  aerofoils  in  general  use  the  critical  angle  is  usually  about 
1 6°,  the  corresponding  lift  coefficient  varying  from  '45  to  '70. 
The  maximum  Lift/Drag  ratio  occurs  at  about  4°  angle  of 
incidence  and  varies  in  value  between  15  and  18.  The  minimum 
drag  so  far  obtained  is  about  '006.  It  is  usual  to  incorporate  all 
these  three  curves  on  one  chart,  as  shown  in  Fig.  40. 

Pressure  Distribution  over  an  Aerofoil. — Having  con- 
sidered the  characteristic  points  of  an  aerofoil,  it  is  desirable  to 
investigate  the  nature  of  the  airflow  producing  these  charac- 
teristics, and  to  examine  the  effect  upon  this  flow  of  changes  in 
the  shape  of  the  aerofoil. 

To  establish  the  principles  underlying  the  remarkable 
efficiency  of  a  good  aerofoil  section  as  compared  with  an 
inclined  flat  plate,  the  N.P.L.  investigated  the  distribution  of 
pressure  over  the  surface  of  an  aerofoil.  The  following  infor- 
mation is  taken  from  the  Reports  for  the  years  1911-1912-1913. 

In    order   to    make   a   thorough    analysis   of    the    pressure 
distribution  over  a   large  range  of  angles  of  incidence,  it  was 
found  advisable  to  limit  the  scope  of  the  experiments  to  three 
different  shapes,  namely — 
i.  A  flat  plate. 

ii.  An  aerofoil  with  both  surfaces  cambered. 

iii.  An  aerofoil  with  the  top  surface  only  cambered. 

The  models  used  are  illustrated  in  Fig.  41,  the  flat  plate 
being  made  of  thin  steel  "02"  thick,  12"  long,  and  2j"  wide, 
while  the  other  two  models  were  moulded  with  wax  upon  thin 
brass  sheet  curved  to  the  desired  shape,  12"  long  by  2|"  wide, 
the  upper  surfaces  of  these  two  models  being  exactly  similar. 
The  pressure  was  observed  at  eight  different  points  along  the 
median  section,  the  position  of  the  holes  being  indicated  in 
Fig.  41.  These  holes  were  1/64"  in  diameter  and  each  com- 
municated when  under  observation  with  a  manometer  by  means 
of  a  length  of  tubing.  All  the  holes  except  the  one  under  test 


56  AEROPLANE    DESIGN 

were  plugged  with  plasticine,  and  the  whole  apparatus  was 
designed  to  interfere  as  little  as  possible  with  the  flow  of  the 
air  around  the  aerofoil.  The  speed  of  the  wind  stream  was 
measured  in  the  usual  way  by  observing  the  pressure  difference 
shown  by  the  Pitot  tube,  and  was  found  to  be  about  17  feet  per 
second. 

N?    1  .'   ?          3 +  5  67 


N°2 


,    2 

N95 

FIG.  41. — Aerofoil  Sections. 

The  pressure  diagrams  obtained  for  these  three  model  aero- 
foils are  shown  in  Fig.  42.  Ordinates  below  the  datum  line 
indicate  negative  pressure  or  suction,  while  those  above  indicate 
positive  pressure.  It  will  be  seen  that  for  ordinary  flight  angles 
both  the  negative  pressure  over  the  top  surface  and  the  positive 
pressure  over  the  bottom  surface  reach  a  maximum  very  near 
to  the  leading  edge  and  fall  away  almost  to  zero  at  the  trailing 
edge,  and  for  certain  angles  of  incidence  they  even  change  sign. 
It  is  this  phenomenon  which  accounts  for  the  position  of  the 
centre  of  pressure — the  point  on  the  chord  at  which  the  resultant 
force  acts — being  much  ahead  of  the  centre  of  the  chord  for 
flight  angles,  and  which  points  to  the  necessity  for  making  the 
leading  edge  of  an  aerofoil  very  much  stronger  than  the  trailing 
edge.  Applying  these  results  to  full-size  wings,  the  force  per 
square  foot,  at  an  angle  of  incidence  of  10°  and  a  speed  of 
60  miles  per  hour,  is  about  35  Ibs.  at  the  leading  edge  and  only 
2  Ibs.  at  the  trailing  edge. 

The  observations  show  that  for  each  aerofoil  there  is  a 
critical  angle  above  which  the  pressure  over  the  upper  surface, 
after  passing  through  a  period  of  extreme  unsteadiness, 


THE    PROPERTIES   OF   AEROFOILS 


57 


A. 


1 


B     5 


I 
-I 


FIG.  42. — Distribution  of  Pressure  on  Median 
Section  of  Aerofoils  Nos.  i  and  3. 


58  AEROPLANE    DESIGN 

becomes  uniform.  For  angles  below  the  critical  angle  the 
pressure  over  both  surfaces  varies  with  the  angle  of  incidence 
according  to  definite  laws,  but  after  the  unsteady  region  is 
passed  the  distribution  over  the  upper  surface  becomes  uniform, 
while  pressure  on  the  lower  surface  falls  off  to  an  extent 
sufficient  to  cause  a  change  of  sign  near  the  trailing  edge.  A 
determination  of  the  lift  and  drag  on  these  aerofoils  was  also 
carried  out,  and  the  results  are  shown  plotted  in  Fig.  43  (a)  and 
(b).  From  these  curves  it  appears  that  the  critical  angle,  above 
which  the  pressure  distribution  becomes  unsteady,  corresponds 
to  the  critical  angle  of  the  lift  curve  at  which  there  is  a  falling 
off  in  the  lift  and  a  large  increase  in  the  drag.  This  indicates 
that  these  phenomena  are  due  to  the  sudden  alteration  in  the 


Aerofoil  No.1. 
Aerofoil  No. 2. 
Aerofoil  No. 3. 


o-ao 


0-10 


r 

o 


o-oo 


0*         5*        10*       15°       £0'      25* 

Angle  of  Incidence. 


-o-io 


Aerofoil  No.3: 


AeropoilNol^ 


r 


(b) 


o*     5°    to*    /5°    eo* 
Angle  op  Incidence. 


FIG.  43.  —  Lift  and  Drag  Curves  for  three  Aerofoils. 


pressure  distribution  over  the  upper  surface,  owing  to  a  break- 
down in  the  character  of  the  fluid  flow  in  the  neighbourhood  of 
this  angle.  The  value  of  the  critical  angle  and  the  amount 
of  change  that  occurs  at  this  point  is  largely  influenced  by 
changing  the  position  of  the  maximum  ordinate  of  the  aerofoil 
section,  as  will  be  seen  shortly.  A  striking  peculiarity  illus- 
trated by  these  pressure  distribution  curves  is  that  it  is  possible 
to  have  a  very  high  negative  pressure  or  suction  near  the 
leading  edge  when  the  angle  of  incidence  is  such  that  a  positive 
pressure  would  have  been  anticipated.  The  principle  under- 
lying this  departure  from  expected  conditions  is  known  as  the 
'  Phenomenon  of  the  Dipping  Front  Edge,'  the  explanation 
being  that  the  stream-lines  approaching  the  leading  edge  are 
deflected  upwards  before  reaching  it,  and  consequently,  although 
the  local  angle  of  incidence  with  the  general  wind  direction  may 
be  positive,  the  actual  angle  made  with  the  local  wind  is 


THE    PROPERTIES    OF   AEROFOILS 


59 


negative.     This  upward  deflection  of  the  stream-lines  is  accom- 
panied by  the  formation  of  a  general  low-pressure  region  above 


FIG.  44. — Flow  past  an  Aerofoil  Section,  showing  Development 
of  Eddy  Motion  with  Increase  of  Angle  of  Incidence. 

and  a  high-pressure  region  below  the  aerofoil.  The  photographs 
reproduced  in  Fig.  44  show  the  effect  of  the  disturbance  for 
different  angles  of  incidence. 

Aerofoil  Efficiency. — For  an  aerofoil  to  be  of  practical 
value  it  is  essential  that  at  some  angle  of  incidence  there  should 
exist  a  high  value  of  the  ratio  of  L/D,  accompanied  by  a  high 
value  of  the  lift  coefficient.  In  the  case  of  the  flat  plate, 
although  the  maximum  ratio  of  L/D  may  be  high  at  ordinary 
angles,  the  corresponding  value  of  the  lift,  as  shown  by  Fig.  43 
(a),  is  much  too  low  for  practical  purposes.  The  total  lift  on 
the  aerofoil  is  seen  from  the  same  figure  to  be  much  greater 
than  that  for  the  flat  plate,  and  there  is  also  a  much  greater 


60  AEROPLANE   DESIGN 

range  between  the  angle  of  no  lift  and  the  critical  angle,  thus 
allowing  much  more  latitude  for  adjustment  during  flight.  The 
most  important  consideration  leading  to  the  greater  efficiency  of 
the  aerofoil  is  as  follows  :  Whereas  the  resultant  force  on  a  flat 
plate  can  never  act  forwards  of  a  normal  to  itself,  a  good  aero- 
foil section,  on  account  of  the  upward  deflection  of  the  stream- 
lines shown  in  Fig.  44,  and  the  consequent  pressure  distribution 
over  the  front  portion  of  the  aerofoil,  can  and  usually  does  have 
a  resultant  force  upon  it  acting  in  a  direction  well  forward  of 
the  normal  to  the  chord.  These  cases  are  illustrated  in  Figs.  35 
and  45.  If  the  surface  of  the  flat  plate  offered  no  resistance  to 


FIG.  45. 

the  airflow,  which  corresponds  to  a  condition  of  maximum 
efficiency,  the  resultant  would  be  exactly  perpendicular  to  the 
plate.  The  effect  of  skin  friction,  however,  is  such  that  the 
resultant  acts  behind  the  normal  to  the  chord.  For  the  aerofoil 
the  pressure  distribution  is  such  that  the  resultant  acts  forward 
of  the  normal  to  the  chord.  Resolving  normally  and  along  the 
chord,  we  therefore  have  a  component  acting  along  the  chord 
practically  in  the  opposite  direction  to  the  drag  force,  thus 
reducing  the  value  of  the  total  drag,  and  thereby  increasing  the 
value  of  the  L/D  ratio.  The  increased  efficiency  of  an  aerofoil 
is  principally  dependent  upon  the  production  of  this  component 
acting  in  opposition  to  the  drag.  Reference  to  the  curves  in 
Fig  42  shows  that  this  is  due  to  the  uneven  pressure  distribution 
over  the  upper  surface.  If  the  pressure  distribution  were 
uniform,  this  opposing  component  would  disappear  entirely  and 
the  drag  would  be  greatly  increased,  and  this  is  actually  what 
occurs  after  the  critical  angle  is  passed.  The  more  pronounced 
this  uneven  pressure  distribution  effect  can  be  made  without 
causing  a  breakdown  in  the  airflow,  the  more  efficient  the 
aerofoil  becomes. 


THE    PROPERTIES    OF    AEROFOILS 


61 


Pressure  Distribution  over  the  Entire  Surface  of  an 
Aerofoil. — The  experiments  just  described  relating  to  the 
pressure  distribution  over  the  median  section  of  a  model  aero- 


7.                6,                  5.                  4.                   3, 

e. 

t 

3" 

{ 

A-                                      6 

c 

ft- 

1 
SL. 

• 

,, 

18 


FIG.  46. — Plan  and  Section  of  Aerofoil, 
showing  Observation  Points. 

foil  were  subsequently  extended  to  cover  the  entire  surface,  the 
observations  being  made  at  four  other  sections,  all  compara- 
tively near  to  the  wing-tips,  as  well  as  at  the  median  section. 


Ah  SccHon  A  . 


o       -j      i-o      is      a-o 

Scale    of  Absolul-c   Pressures. 


Ar  SecMon  E 


0°      Incidence. 


4°    Incidence. 


12*    Incidence. 

FIG.  47. — Curves  showing  Pressure  Distribution  over  Aerofoil 
at  Median  and  End  Sections. 

The  positions  of  these  observation  points  are  indicated  in 
Fig.  46,  and  the  results  obtained  are  shown  in  Fig.  47.  Positive 
pressures  are  denoted  by  normals  drawn  downwards  from  the 


62  AEROPLANE    DESIGN 

upper  or  lower  surface,  and  negative  pressures  by  normals 
drawn  upwards.  These  pressures  are  given  in  absolute  units. 
To  convert  to  pounds  per  square  foot  at  V  miles  per  hour, 
multiply  by  -00510  V2. 

The  pressure  distribution  is  shown  for  three  angles  of 
incidence,  o°,4°,and  12°,  for  the  median  section  and  the  extreme 
end  section,  side  by  side  in  order  to  give  a  clearer  conception  of 
the  very  different  airflow  existing  at  these  two  sections.  It  is 
found  that  the  points  of  highest  pressure  on  the  aerofoil 
gradually  recede  from  the  leading  edge,  until  in  the  neighbour- 
hood of  the  wing-tip  the  maximum 'pressures  occur  close  to  the 
trailing  edge  and  are  due  to  suction  entirely.  As  a  result  of 
this  the  direction  of  the  resultant  lift  force  instead  of  being 
inclined  toward  the  direction  of  motion,  is  inclined  in  the 
opposite  way,  and  hence  its  component  in  the  direction  of  motion 
increases  the  drag  force.  The  value  of  the  drift  is  a  minimum 
at  the  central  section  and  increases  gradually  towards  the  wing- 
tips  and  then  rises  very  rapidly  at  the  extreme  ends.  The  lift 
coefficient  falls  off  considerably  near  the  tips,  its  value  only 
being  about  one-half  that  at  the  central  section.  This  is  due  to 
the  lateral  escape  of  the  air  on  the  under  side  of  the  wing  and 
the  influx  of  air  above  the  wing.  The  result  of  this  variation  in 
the  characteristics  of  the  aerofoil  section  at  the  wing-tips  is  a 
reduction  in  the  L/D  ratio  of  the  \\ing  as  a  whole  ;  that  is,  the 
efficiency  of  the  supporting  surface  is  diminished  owing  to  this 
effect,  which  is  often  called  the  *  End  Effect.' 

Full-scale  Pressure  Distribution  Experiments.* — In  a 
paper  read  before  the  Aeronautical  Society,  Captain  Farren 
gave  an  account  of  the  investigation  of  the  distribution  of 
pressure  over  the  wings  of  a  full  size  machine  when  in  flight. 
The  method  adopted  was  very  similar  to  that  used  for  model 
aerofoils.  A  number  of  small  tubes  were  run  through  the  wings,, 
with  the  outer  ends  open  and  fixed  at  the  point  in  the  surface 
of  the  wing  at  which  it  was  desired  to  measure  the  pressure. 
The  inner  ends  of  the  tubes  were  connected  to  manometer 
tubes  so  arranged  that  pressure  differences  could  be  recorded 
photographically.  A  diagrammatic  sketch  of  the  arrangement 
is  shown  in  Fig.  48.  As  in  the  model  experiments,  all  the  holes 
except  the  one  under  observation  at  the  moment  were  sealed 
up,  and  great  difficulty  was  encountered  in  ensuring  that  there 
were  no  leaks  in  the  tubes.  Difficulty  was  experienced  in 
comparing  the  results  with  those  obtained  in  model  aerofoil 
experiments,  as  it  was  not  possible  to  determine  the  attitude 

*  Aeronautical  Journal,  February,  1919. 


THE    PROPERTIES   OF   AEROFOILS 


of  the  machine  exactly,  but  by  installing  a  yawmeter  in  a 
vertical  plane,  it  may  be  possible  to  record  the  correct  angle  of 
incidence  on  the  photographic  record. 


R»b. 


FIG.  48.  —  Arrangement  of  Manometer  Tubes  for  Investigation 
of  Pressure  Distribution  in  Full-scale  Machines. 

Fig.  49  shows  a  comparison  of  the  pressures  obtained  in  a 
test  upon  a  model  biplane  in  the  wind  tunnel,  and  corresponding 
full-scale  machine  tested  in  the  manner  indicated  above. 

Aspect  Ratio.  —  The  pressure  distribution  diagrams  given* 
in  Fig.  47  lead  one  to  expect  that  the  efficiency  of  a  wing 
surface  will  be  increased  by  an  increase  in  aspect  ratio. 
Table  XVI.  shows  that  this  is  precisely  what  occurs. 


Aspect 
ratio. 


TABLE 

XVI.  —  INFLUENCE  OF  ASPECT  RATIO. 
Angles  of  Incidence. 

3° 

6° 

Lift 

L4P 

Lift 

L/D 

•     Lift 

•60 

'47 

...        .62 

*54 

'60 

•70 

•58 

•••        73 

•64 

...        78 

•84 

73 

...        "85 

'77 

...        -90 

*94 

•86 

•••       '95 

•90 

...        '96 

I  '00 

I'OO 

I'OO 

I'OO 

1*00 

1-05 

i  '06 

i  "04 

no 

...      1-04 

i  -08 

i  '09 

...      i'o8 

1-16 

...      i  '08 

9° 


L/D 

'55 

•72 

'S3- 
•92 

I'OO 
I'OO/ 

1-15 


64 


AEROPLANE   DESIGN 


An   aspect   ratio    of  6  has   been    taken    as    a   standard    of 
reference  and  the  lift,  and  L/D  of  other  aspect  ratios  expressed 


(V 

Q. 


0-8 
04 
O 

0-4 
O 

-04 


-0* 
-1-2 
-1-6 


o-e 

O-4- 


-0-8 


-« 


UPPER     WING 


Ha 


59° 


0° 


8-1° 

LOWER    WING 
2-15° 


8-3° 


1H° 


Full   Scale 
Model 


FIG.  49. — Comparison  of  Pressure  Distribution 
on  Model  and  Full-scale  Biplane. 

in   terms  of  this   unit.      It   will   be   seen   that   the   L/D    ratio 
increases   continuously  with  aspect   ratio.     The  actual  figures 


THE   PROPERTIES   OF   AEROFOILS  65 

are  graphed  in  Fig.  50,  from  which  it  will  be  seen  that  the  value 
is  about  10  for  an  aspect  ratio  of  3,  and  increases  to  about  15*5 
for  an  aspect  ratio  of  8.  The  maximum  lift  coefficient  remains 
practically  constant,  the  increased  efficiency  at  high  values  of 
aspect  ratio  being  due  to  reduced  drag  coefficients.  It  will  also 
be  seen  from  this  figure  that  as  the  aspect  ratio  becomes  less, 
the  angle  of  no  lift  occurs  earlier. 

Since  models  of  aerofoils  and  complete  wing-spans  are 
almost  invariably  tested  with  an  aspect  ratio  of  6,  it  is  only 
necessary  to  multiply  the  values  given  for  the  lift,  and  L/D 


Angle    of    Inc'derx* 


FIG.  50. — -Effect  of  Aspect  Ratio  upon  Lift/Drag  Ratio. 

coefficients  by  the  appropriate  factor  in  Table  XVI.,  in  order 
to  obtain  the  correct  value  for  any  aspect  ratio  between  2  and  8. 

The  Relative  Importance  of  the  Upper  and  Lower 
Surfaces  of  an  Aerofoil. — The  pressure  distribution  curves 
given  in  Fig.  42  show  that  at  ordinary  angles  of  flight  the 
negative  pressure  or  suction  over  the  upper  surface  is  much 
greater  numerically  than  the  positive  pressure  on  the  lower 
surface.  In  the  case  of  the  flat  plate,  the  upper  surface  con- 
tributes about  75%  of  the  total  force  normal  to  the  chord  over 
the  greater  part  of  the  range  of  angles  under  consideration, 


66  AEROPLANE   DESIGN 

while  for  aerofoils  the  upper  surface  contributes  practically  all 
the  normal  force  at  from  o°  to  4°,  and  quite  75%  of  this  force 
at  12°.  Since  at  these  angles  the  force  normal  to  the  chord  is 
scarcely  distinguishable  from  the  lift,  it  can  be  stated  as  a 
general  rule  that  the  lower  surface  of  any  aerofoil  never  pro- 
vides more  than  25%  of  the  lift.  This  is  an  important 
consideration  from  trie  constructional  point  of  view,  in  that 
it  shows  the  necessity  of  securing  the  canvas  forming  the 
upper  surface  of  the  wing  very  firmly  to  the  ribs  in  order  to 
prevent  it  being  torn  away  in  an  upward  direction.  There  are 
no  forces  parallel  to  the  chord  in  the  case  of  the  flat  plate  and  in 
that  of  the  aerofoil  with  flat  undersurface  excepting  skin  friction. 
For  the  cambered  undersurface  the  lower  surface  contributes 
only  I2j%  of  the  total  force  at  12°,  while  for  angles  below  7° 
the  force  on  it  is  in  the  direction  of  positive  drag  and  is 
therefore  disadvantageous. 

An  examination  of  the  pressure  distribution  curves  for  the 
aerofoils  and  plate  makes  it  possible  to  compare  the  variation 
of  pressure  distribution  upon  (a)  a  flat  lower  surface  coupled 
both  with  a  flat  and  a  convex  upper  surface,  and  (b)  a  convex 
upper  surface  coupled  both  with  a  flat  and  a  concave  lower 
surface.  As  a  result,  it  is  found  that  the  forces  on  the  upper 
surfaces  of  aerofoils  are  only  slightly  affected  by  change  of 
shape  in  the  lower  surface.  For  the  lower  surface,  however, 
it  is  found  that  the  percentage  change  due  to  variation  of  the 
form  of  the  upper  surface  is  considerable ;  but  as  these  forces 
are  small  in  magnitude,  this  change  has  very  little  influence 
upon  the  total  forces.  These  results  demonstrate  that  the 
upper  surface  of  an  aerofoil  contributes  by  far  the  greater 
part  of  the  total  force  acting  upon  the  aerofoil,  and  that 
the  pressure  distribution  is  practically  independent  of  the 
shape  of  the  lower  surface,  provided  that  it  is  not  convex. 

As  a  corollary,  the  best  form  of  upper  surface  can  be  deter- 
mined in  conjunction  with  some  standard  lower  surface,  say  a 
flat  one,  and  when  this  has  been  completed,  the  lower  surface 
can  be  varied  without  appreciably  upsetting  the  results  obtained 
for  the  upper  surface.  A  detailed  investigation  upon  these  lines 
was  carried  out  by  the  N.P.L.  in  order  to  determine  the  best 
form  of  aerofoil. 

The  lift  and  drag  of  a  series  of  aerofoils  were  measured, 
variations  in  the  shape  of  these  aerofoils  being  made  according 
to  the  following  plan  : — 

I.  Aerofoils  with  a  plane  under  surface,  but  with  variable 
camber  of  upper  surface. 


THE    PROPERTIES    OF    AEROFOILS 


67 


2.  Aerofoils  possessing  the  same  form  of  upper  surface,  but 

with  variable  camber  of  lower  surface. 

3.  Aerofoils  in  which  the  position  of  the  maximum  ordinate 

was  altered. 

As  the  results  of  these  experiments  are  of  considerable 
practical  value  in  the  design  of  aerofoils  for  specific  purposes, 
they  will  be  given  fully. 

Determination  of  the  Lift  and  Drag  of  a  series  of 
Aerofoils  with  plane  lower  surface  and  variable  camber 
of  upper  surface. — The  variation  of  camber  of  these  aerofoils 
was  obtained  by  varying  the  height  of  the  maximum  ordinate — 


—  .29    of   chord    - 

FIG.  51. — Dimensions  of  Aerofoils  of  Variable  Camber. 

kept  in  the  same  position  at  '29  of  the  chord  from  the  leading 
edge — from  "063"  to  -437' '.  This  ordinate  is  then  divided  into 
ten  equal  parts  and  abscissae  drawn  in  the  positive  and  negative 
direction  from  each  point  of  division.  The  lengths  of  these 
abscissae  remained  constant  for  the  series  of  aerofoils.  The 
scheme  is  shown  in  Fig.  51,  and  the  resulting  aerofoils  are 
shown  in  Figs.  52  and  53.  The  numbers  attached  to  the 
aerofoils  are  in  order  of  the  depth  of  the  maximum  ordinate. 
The  length  of  each  aerofoil  was  15"  and  the  width  was  2-5". 
The  velocity  of  the  air  stream  in  the  wind  tunnel  during  the 
tests  was  20  miles  per  hour.  The  result  of  the  observations 
is  shown  by  Figs.  52  and  53.  The  aerofoil  with  the  maximum 
ordinate  begins  to  lift  at  an  angle  of  —  7°,  the  maximum  lift 
being  obtained  at  an  angle  of  6°.  With  diminishing  camber 


68 


AEROPLANE   DESIGN 


the  angles  of  no  lift  and  of  maximum  lift  become  greater,  and 
the  decrease  of  the  lift  coefficient  after  passing  the  critical 
angle  becomes  much  less  marked.  For  all  the  aerofoils  the 
L/D  curves  show  maxima  between  3°  and  4°,  but  the  actual 
values  of  these  maxima  vary  greatly.  As  the  camber  changes, 
the  L/D  ratio  approaches  and  passes  a  maximum  in  the 
neighbourhood  of  15,  the  corresponding  camber  being  about 
one  in  twenty. 

FIG 


NO   I 


NO  2 


HO  3 


ANQUE  OF   INCIDENCE 


FIG.  52.  —  Aerofoils  with  Variable  Camber  of  Upper  Surface. 

From  an  aerodynamical  point  of  view,  the  most  important 
characteristics  of  an  aerofoil  are  : 

(i)  The  maximum  L/D  ratio  obtainable. 
(ii)  The  value  of  the  lift  coefficient  at  the  angle  of  maximum 

L/D. 

(iii)  The  ratio  of  the  value  of  the  lift  coefficient  at  the  angle 
of  maximum  L/D  to  the  value  of  the  lift  coefficient 
at  the  critical  angle. 

It  will  be  seen  from  the  curves  that  the  aerofoils  having  a 
high  maximum  value  for  L/D  ratio  have  a  low  value  for  the 
corresponding  lift  ;  but  since  the  ratio  of  this  lift  value  to  the 


THE   PROPERTIES   OF   AEROFOILS 


69 


maximum  lift  coefficient  is  also  low,  such  aerofoils  are  suitable 
for  variable  speed  machines.  Table  XVII.  was  prepared  to 
indicate  the  best  camber.  It  was  assumed  that  the  aerofoils  had 
been  arranged  at  such  angles  of  incidence  as  to  give  the  same 
lift  coefficient  at  the  same  speed.  The  lift  coefficient  corre- 
sponding to  usual  practice  is  about  0*25,  and  for  this  value  the 
best  L/D  ratio  is  15,  and  the  camber  required  is  '055.  If  for 
constructional  purposes  it  is  desired  to  use  a  larger  camber, 
column  5  shows  the  extent  to  which  this  may  be  done  without 
decreasing  the  L/D  ratio  by  more  than  10%. 


Afc-7 


FIG.  53. — Aerofoils  with  Variable  Camber  of  Upper  Surface. 


Lift  coefficient 
absolute. 

"10 


'20 

•25 
•30 

'35 
•40 

•45 


TABLE 

XVII.—  CAMBER. 

Camber  for 

Corresponding         Maximum 

maximum  L/D. 

maximum  L/D. 

lift. 

very  small     .. 

— 

— 

less  than  '02  .  . 

. 

— 

•043 

15-0     -    ... 

o'5 

*°55 

15-0         ... 

o'57 

•06 

14-5 

°'59 

•06 

14*0 

°'59 

•06 

•          I3'3         ••• 

°'59 

•07 

I2'2 

o'6o 

•08 

in 

o'6o 

Camber  for  L/D 
-  10%  decrease. 


o'o6 

0-08 

0-093 

0*106 

0*115 

0-137 


AEROPLANE    DESIGN 


Determination  of  the  Lift  and  Drag  of  a  Series  of 
Aerofoils  with  the  same  Upper  Surface  and  Variable 
Camber  of  Lower  Surface. — The  scheme  of  these  aerofoils  is 
shown  in  Fig.  54,  together  with  the  resulting  aerofoils.  Aero- 
foil 4  of  the  previous  series  (see  Figs.  52  and  53)  was  taken  as 
the  basis,  and  camber  given  to  the  lower  surface  by  gradually 
increasing  the  height  of  the  maximum  ordinate  from  the  chord 
line  according  to  the  dimensions  attached  to  Fig.  54.  It  was 


FIG.  54. — Aerofoils  with  Variable  Camber  of  Lower  Surface. 

found  that  the  L/D  ratios  are  practically  unaltered  by  camber 
of  the  lower  surface.  The  value  of  the  lift  coefficient,  as  will  be 
seen  from  Fig.  54,  increases  steadily  with  increase  of  camber ; 
but  the  variation  is  small,  a  maximum  increase  of  17%  being 
obtained  at  the  angle  of  maximum  L/D.  The  critical  angle  is 
unaltered  by  increase  of  camber  on  the  lower  surface,  and  the 
fall  in  the  lift  coefficient  after  this  angle  is  passed  becomes  less 
as  the  camber  is  increased. 


THE   PROPERTIES   OF   AEROFOILS  71 

Determination  of  the  Lift  and  Drag  of  a  Series  of 
Aerofoils,  the  Position  of  the  Maximum  Ordinate  being 
varied. — The  sections  were  all  developed  from  one  chosen 


section  by  altering  the  position  of  the  maximum  ordinate  of  the 
upper  surface,  the  lower  surface  being  kept  plane,  and  are 
illustrated  in  Fig.  55.  The  column  headed  '  Ratio  x/c'  gives 


72  AEROPLANE    DESIGN 

the  position  of  the  maximum  ordinate,  and  the  column  headed 
*  Design  index '  gives  the  value  of  the  index  '  a '  in  the  expression 
x  =  J  c  (o*76)a.  The  original  series  contained  only  members 
whose  design  indices  were  o,  I,  2,  3,  4,  and  the  other  members 
were  introduced  as  occasion  required  in  order  to  preserve  con- 
tinuity in  the  observations.  The  cutves  obtained  from  the 
observations  on  the  nine  aerofoils  are  also  shown  in  Fig.  55. 
The  most  important  deduction  from  the  experiments  is  that  for 
the  particular  camber  adopted  (o'ioo),  the  greatest  maximum 

T^- 

~  occurs  when  the  position  of  the  maximum  ordinate  is  at 
Kx 

about  one-third  of  the  chord  from  the  leading  edge.  The  main 
variations  in  the  lift  curves  occur  at  angles  above  10°.  Below 
this  angle  the  curves  are  of  the  same  general  character,  although 
they  differ  widely  at  higher  angles,  and  in  certain  cases  are 
greatly  changed  by  minute  changes  of  the  form  of  the  section. 
It  will  be  seen  that  for  aerofoils  o  and  i  there  is  no  defined 
critical  angle,  the  lift  following  a  continuous  smooth  curve 
having  a  flat  maximum  between  16°  and  18°.  In  the  next 
aerofoil,  design  index  i£,  a  region  corresponding  probably  to 
uncertain  flow  is  observed  between  17°  and  18°,  the  lift  coefficient 
oscillating  between  0*67  and  0*54.  The  next  aerofoil,  design 
index  I J,  shows  this  effect  more  strongly  marked  ;  while  suc- 
ceeding aerofoils  show  this  peculiar  dip  in  the  lift  curves 
becoming  steadily  wider  and  shallower.  The  wind  velocity 
for  these  experiments  was  28  feet  per  second.  With  an 
increased  velocity  this  dip  was  practically  eliminated. 

It  is  interesting  to  note  that  all  the  more  complicated 
changes  in  the  value  of  the  lift  coefficient  occur  with  the 
aerofoils  whose  indices  are  between  I  and  2  ;  that  is,  they 
correspond  to  a  movement  in  the  position  of  the  maximum 
ordinate  of '012  of  the  chord,  and  that  the  form  of  the  curve  is 
very  sensitive  to  minute  changes  of  the  section.  The  sudden 
change  in  the  lift  coefficient  at  the  critical  angle  is  always 
accompanied  by  a  change  in  the  drag,  an  increase  in  lift  being 
associated  with  decrease  of  drag  and  vice  versa.  This  indicates 
that  the  change  is  due  to  a  sudden  alteration  in  the  flow  from 
an  efficient  to  an  inefficient  type. 

T£ 

The  ratio  of  -^/-  increases  as  the  maximum  ordinate  moves 

Kx 

from  the  centre  of  the  chord,  until  its  position  reaches  a  point 
about  one-third  of  the  chord  from  the  leading  edge.  It  would 
seem  preferable,  however,  to  avoid  the  uncertainty  of  flow  above 
described  and  to  use  an  aerofoil  having  its  maximum  ordinate 


THE    PROPERTIES    OE   AEROFOILS  73 

at  about  '375  of  the  chord  from  the  leading  edge.     This  results 


in  a  reduction  of  the  maximum 
aerofoil,  from  13*9  to  13*2. 


jr 


,  for  this  particular  type  of 


Effect  of  thickening  the  Leading  Edge  of  an  Aerofoil. 
—  These  experiments  were  devised  in  order  to  show  the  way 
in  which  the  behaviour  of  an  ordinary  aerofoil  is  influenced  by 
substituting  a  thickened  for  a  sharp  leading  edge.  The  sections 


FIG.  56. — Aerofoils  of  Variable  Thickness  of  Leading  Edge. 

of  the  aerofoils  are  shown  in  Fig.  56.  All  the  aerofoils  are 
identical  behind  the  maximum  ordinate,  and  the  camber  and 
chord  remain  unchanged  throughout  the  series.  The  results  of 
the  observations  are  shown  plotted  in  Fig.  56,  from  which  it  will 
be  seen  that  the  maximum  L/D  decreases  steadily  as  the  thick- 
ness of  the  nose  increases,  showing  that  the  efficiency  of  an 
aerofoil  section  is  impaired  by  thickening  the  leading  edge. 
The  lift  is  not  greatly  ^affected  below  angles  of  8°,  but  above  this 
angle  the  form  of  the  curve  is  sensitive  to  the  increasing  thick- 
ness of  the  nose.  The  final  effect  on  the  lift  is  to  cause  the 
critical  angle  to  occur  much  earlier  and  to  flatten  out  the  lift 
curve  after  this  angle  is  reached. 


74 


AEROPLANE   DESIGN 


Effect  of  thickening  the  Trailing  Edge  of  an  Aerofoil. — 
These  experiments  were  undertaken  in  order  to  determine  the 
extent  to  which  an  aerofoil  can  be  thickened  in  the  neighbour- 
hood of  the  rear  spar  without  materially  affecting  its  aero- 
dynamical properties,  such  extra  thickness  being  very  desirable 
in  this  region  from  a  constructional  point  of  view.  The  sections 
of  the  aerofoils  used  are  shown  in  Fig.  57,  No.  3  of  the  series 
being  the  same  as  the  R.A.F.  6  aerofoil  illustrated  in  Fig.  40. 
The  observations  are  shown  plotted  in  Fig.  57,  from  which  it 


10* 

OF  INCIDENCE 


FIG.  57. — Aerofoils  with  Variable  Thickness  of  Rear  Portion. 

appears  that  the  lift  coefficient  is  not  much  affected  at  angles 
greater  than  7°,  while  the  L/D  curves  show  a  steady  improve- 
ment as  the  thickness  diminishes. 

Centre  of  Pressure. — The  position  of  the  centre  of  pressure 
(C.P.)  of  an  aerofoil  is  defined  as  the  point  at  which  the  line  of 
resultant  force  over  the  aerofoil  section  cuts  the  chord.  Since 
the  pressure  distribution,  and  hence  tlie  total  force  over  the 
aerofoil,  varies  with  the  angle  of  incidence  in  the  manner  already 
described  and  illustrated  in  Fig.  47,  it  follows  that  the  C.P.  will 
also  vary  in  its  position  along  the  chord-line.  It  has  been  seen 
that  with  increasing  angle  of  incidence  up  to  the  critical  angle, 


THE   PROPERTIES    OF   AEROFOILS 


75 


the  pressure  over  the  front  portion  of  the  aerofoil  is  greater  than 
that  over  the  rear  portion,  and  as  a  result  the  C.P.  moves 
forward.  The  importance  of  this  fact  from  the  practical  point 
of  view  must  be  clearly  realised,  because  the  C.P.  of  a  wing 
section  may  be  regarded  as  the  point  at  which  the  resultant  lift 
of  the  supporting  surfaces  acts.  The  position  of  the  centre  of 
gravity  (C.G.)  of  the  machine,  however,  remains  unaltered, 
hence,  although  for  one  particular  angle  of  incidence  the  line  of 
resultant  lift  can  be  arranged  to  pass  through  the  C.G.,  for  all 


FIG.  58. — Travel  of  the  Centre  of  Pressure. 

other  angles  there  will  be  a  Lift/Weight  couple  introduced. 
Increasing  divergence  from  the  position  of  coincidence  of  the 
C.P.  with  the  C.G.  will  tend  to  make  this  couple  greater,  and 
consequently  the  system  will  become  unstable.  The  function  of 
the  tail  plane  is  to  provide  the  necessary  righting  moment,  in 
order  that  the  machine  may  be  capable  of  steady  flight  over  the 
required  range  of  angle  of  incidence.  A  knowledge  of  the 
variation  of  the  position  of  the  C.P.  is  therefore  essential  for  a 
correct  setting  of  the  tail  in  order  to  obtain  stability.  It  is 
interesting  to  recall  in  this  connection  that  Lilienthal,  in  his 
glider  experiments,  obtained  stability  by  moving  his  body  over 


76 


AEROPLANE    DESIGN 


the  lower  plane,  thus  countering  the  travel  of  the  C.P.  by  a 
corresponding  movement  of  the  C.G.  This  travel  of  the  C.P. 
has  also  an  important  bearing  upon  the  design  of  the  wing 
structure,  for  it  gives  rise  to  a  variation  in  the  stresses  of  the 
front  and  rear  spar  bracing  systems  as  the  angle  of  incidence 
increases.  It  is  therefore  necessary  to  stress  the  wing  structure 
for  the  most  extreme  cases  that  occur  over  the  range  of  flying 
angles,  namely, 

(a)  The  most  forward  position  of  the  C.P. 

(b)  The  most  backward  position  of  the  C.P. 


Angle     of    Inc-dencc 

FIG.  59. — Aerofoils  with  Variable  Reflexure  of  Trailing  Edge. 

The  position  of  the  C.P.  is  determined  experimentally  by 
measuring  the  lift,  drag,  and  the  moment  about  the  leading  edge 
of  the  aerofoil  under  consideration  for  various  angles  of  inci- 
dence. A  knowledge  of  the  magnitude  of  the  lift  and  drag 
enables  the  direction  of  the  resultant  force  to  be  obtained  for 
each  position,  and  the  moment  of  this  resultant  force  being 
known,  it  is  a  simple  matter  to  calculate  the  leverage  of  the 
moment.  This  fixes  the  position  of  the  line  of  resultant  force, 
and  consequently  the  position  of  the  centre  of  pressure.  The 
moment  and  C.P.  curves  for  the  R.A.F.  6  aerofoil  are  shown  in 


THE    PROPERTIES    OF   AEROFOILS  77 

Fig.  58.     The  curves  of  lift  and  drag  for  this  aerofoil  were  given 
in  Fig.  40. 

Reflexed  Curvature  towards  the  Trailing  Edge. — This 
research  was  undertaken  principally  with  a  view  to  determining 
the  extent  to  which  a  reflex  curvature  towards  the  trailing  edge 
of  an  aerofoil  would  tend  to  neutralise  the  rapid  movement  of 
the  C.P.  due  to  the  change  of  the  angle  of  incidence.  The 
sections  of  the  aerofoils  used  are  shown  in  Fig.  59,  No.  I  of  the 
series  being  in  the  form  of  the  R.A.F.  6.  The  point  in  the 
sections  at  which  reflexing  was  commenced  was  at  0-4  of  the 
chord  from  the  trailing  edge.  The  same  brass  aerofoil  was  used 
for  all  the  sections,  the  form  being  altered  behind  the  point  of 
reflexure  by  means  of  moulded  wax.  The  curves  for  L/D  and 
travel  of  the  centre  of  pressure  are  shown  in  Fig.  59,  from  which 
it  will  be  seen  that  a  practically  stationary  C.P.  can  be  obtained 
with  an  aerofoil  of  this  type  by  elevating  the  trailing  edge  by 
about  0*042  of  the  chord,  while  the  point  of  reflexure  may  be  at 
any  point  between  0*2  and  0*4  of  the  chord  from  the  trailing 
edge.  This  effect,  however,  is  only  obtained  at  the  sacrifice  of 
about  i2°/Q  of  the  maximum  L/D,  and  about  25%  of  the 
maximum  lift.  The  elevation  of  the  trailing  edge,  the  rate  of 
movement  of  the  C.P.,  and  the  loss  in  the  maximum  value  of 
the  L/D  ratio,  are  connected  by  approximate  linear  laws. 

Interference  of  Aerofoils.  —  Mention  has  already  been 
made  of  the  superior  efficiency  of  the  monoplane  from  an  aero- 
dynamical standpoint,  due  to  the  absence  of  interference  effects 
as  compared  with  the  multiplane.  There  are  three  variables 
to  investigate  when  dealing  with  this  question,  namely,  gap, 
decalage,  stagger. 

We  have  seen  in  Fig.  44  how  the  direction  of  flow  of  the  air 
stream  is  affected  when  quite  a  considerable  distance  away  from 
the  leading  edge  of  an  aerofoil.  It  therefore  follows  that  the 
placing  of  bodies  or  other  aerofoils  in  close  proximity  to  the 
first  aerofoil  will  greatly  affect  the  pressure  distribution.  When 
aerofoils  are  placed  above  one  another/ as  in  the  biplane  and 
triplane,  interference  and  modification  of  the  air  forces  at  once 
results. 

Gap. — The  distance  between  the  superimposed  surfaces  is 
known  as  the  gap,  and  the  ratio  of  gap/chord  is  used  as  a 
measure  thereof.  The  negative  pressure  or  suction  upon  the 
upper  surface  of  an  aerofoil  has  been  found  to  be  very  much 
greater  than  the  positive  pressure  upon  the  under  surface  (see 
Fig.  47),  and  consequently  we  should  expect  to  find  that  the 


78  AEROPLANE   DESIGN 

effect  of  placing  one  aerofoil  over  another  is  to  reduce  the  lift 
and  efficiency  of  the  lower  plane,  and  to  leave  the  upper  plane 
practically  unaffected.  This  follows  upon  the  consideration  that 
the  positive  pressure  on  the  under  surface  of  the  upper  aerofoil, 
and  the  negative  pressure  on  the  top  surface  of  the  lower  aero- 
foil, will  tend  to  neutralise  each  other,  whereas  the  negative 
pressure  on  the  top  surface  of  the  upper  aerofoil,  and  the  positive 
pressure  on  the  bottom  surface  of  the  lower  aerofoil,  will  remain 
practically  unaltered.  The  negative  pressure  or  suction  being 
so  much  more  important,  it  follows  that  the  upper  aerofoil  must 
be  much  less  affected.  This  reasoning  is  borne  out  by  the 
experimental  investigations  which  have  shown  that  practically 
the  entire  loss  due  to  superposition  is  to  be  found  in  the  reduc- 
tion of  the  lift  and  L/D  ratio  of  the  lower  plane.  Further,  it 
may  be  deduced  from  this  that  wing-flaps  are  very  much  more 
effective  when  placed  on  the  upper  plane  than  they  would  be  if 
on  the  lower  ;  also  that  in  a  combination  of  a  high-camber  upper 
plane,  with  a  much  flatter  lower  plane,  the  interference  effects 
would  be  greatly  reduced.  Table  XVIII.  gives  the  biplane 
reduction  factors  for  an  average  aerofoil,  and  is  taken  from  an 
N.P.L.  report. 

TABLE  XVIII. — REDUCTION  COEFFICIENTS  DUE  TO 
BIPLANE  EFFECT. 

Lift.  L/D. 

Gap/Chord.  69             8°  10°  6°  8°  10° 

0*4  ...  -     0*61  0*63  o'62  ...  075  o  81  0*84 

0*8  ...  076  0*77  0*78  ...  o'79  0*82  0*86 

i'o  ...  o'8i  0*82  0*82  ...  0*81  0*84  0/87 

12  ...  0-86  086  0-87  ...  0-85  0-85  0-88 

i'6  ...  0*89  0*89  0-90  ...  o'88  0*89  0-91 

To  obtain  values  for  a  biplane,  multiply  values  for  a  single 
aerofoil  by  the  factors  given.  Note  that  there  is  quite  a 
considerable  effect  when  the  Gap  is  equal  to  the  Chord. 

A  more  recent  investigation  carried  out  in  the  Massachusetts 
Institute  of  Technology*  enables  a  comparison  to  be  made 
between  the  lift  and  L/D  coefficients  and  interference  effects  on 
the  biplane  and  triplane.  The  biplane  and  triplane  models  had 
a  constant  gap  between  the  planes  equal  to  1*2  times  the  chord 
length,  and  there  was  no  stagger  or  overhang.  A  single  aerofoil 
was  first  tested  as  a  standard  for  reference,  and  then  the  addi- 
tional surfaces  were  introduced.  The  lift,  and  drag,  and  L/D 
curves  for  each  case  are  show  in  Fig.  60. 

*  Hunsaker  and  Huff.  Reproduced  by  permission  of  Messrs.  J. 
Selwyn  &  Co. 


THE    PROPERTIES    OF   AEROFOILS 


79 


From  comparison  between  the  curves  it  will  be  seen  that  the 
triplane  and    biplane  give  nearly  the   same  maximum  lift   at 


Lift    Monoplane 
Lift      Biplane 
Lift     Tri  plane. 


Angle   o*     Incidence 

FIG.  60. — Aerodynamical  Properties  of  Superimposed  Aerofoils. 

about  1 6°,  but  that  for  smaller  angles  of  incidence  the  triplane 
lift    is    appreciably    reduced.        The    lift    coefficient    for    the 


8o  AEROPLANE    DESIGN 

monoplane  is  seen  to  be  superior  to  the  other  cases  at  all  angles 
above  zero.  The  drag  coefficient  for  angles  below  12°  is  very 
similar  in  each  case,  but  at  large  angles  of  incidence  the  triplane 
has  a  materially  lower  resistance.  The  curves  of  L/D  show  the 
relative  effectiveness  of  the  wings.  Thus,  the  best  ratio  is  17 
for  the  monoplane,  13-8  for  the  biplane,  and  12*8  for  the  triplane. 
These  values  refer  to  small  angles  of  attack,  and  therefore 
correspond  to  a  high  flight  speed.  Table  XIX.  illustrates  these 
points  clearly,  the  biplane  and  triplane  lift  coefficients  being 
expressed  as  percentages  of  the  monoplane  coefficients. 

TABLE  XIX. — COMPARISON  OF  LIFT  COEFFICIENTS. 

Monoplane.  Biplane.  Triplane.  Monoplane.  Biplane.  Triplane. 

Incidence.  Lift  Lift  %  Lift  %  L/D        L/D  %  L/D  % 

o°     ...  -096  88'8  83-0  ...       8-6         73-2  70-8 

2°     ...  "202  83-8         75'4  ...  i6'8         74*7  69*8 

4°     ...  -284  85-4         75-7  ...  16-8         82-0  76-1 

8°     ...  '427  85*2         77'4  ...  13*8         81*9  80*4 

12°     ...  *545  87^6  81  '2  ...  io'o         95'o  89*0 

16°     ...  -543  98-5  96-4  ...  4'5  124-0  145-0 

Experiments  were  next  undertaken  to  determine  the  distri- 
bution of  load  upon  the  three  wings  of  the  triplane  made  from 
aerofoils  of  R.A.F.  6  profile.  The  results  are  shown  in  Figs.  61 
and  62.  It  appears  that  the  upper  wing  is  by  far  the  most 
effective  of  the  three,  and  that  the  middle  wing  is  the  least 
effective.  This  must  be  due  to  the  interference  with  the  free 
flow  of  air  owing  to  the  presence  of  the  upper  and  lower 
wings.  The  results  are  conveniently  tabulated  as  shown  in 
Table  XX.  :— 

TABLE  XX. — COMPARISON  OF  THE  WINGS  OF  A  TRIPLANE. 

Lift.  L/D. 

Incidence.  Upper.      Middle.      Lower.  Upper.      Middle.      Lower. 

o°  ...  2'68  I'o  1-82  ...  3-63  i*o  2-30 

2°  ...  2-14  I'o  1-75  ...  3-18  i'o  2-13 

4°  ...  1*91  i'o  1^64  ...  2*59  i'o  1*69 

8°  ...  1-56  i-o  1-36  ...  1-49  i'o  i'37 

12°  ...  1*56  1*0  1*31  ...  1*30  i'o  i '34 

16°  ...  1*49  i*o  1*20  ...  1*22  i'o  i'i7 

It  will  be  noticed  that  the  middle  wing  has  been  taken  as  a 
standard  of  comparison,  its  lift  and  L/D  being  denoted  by  unity. 

A  further  important  instance  of  interference  is  to  be  found 
in  the  case  of  the  tail  plane.  The  air  stream  is  deflected  from 
the  main  wing  planes  of  a  machine  and  takes  a  downward 


Upper 
Lower 


Rane 
Plame 


Tri  plane 


Angle    of      Incidence 


Trip  lane 


•  Biplane 


20' 


5-  10*  IS*  20* 

Angle     of     Incidence 

FIG.  61. — Lift  and  C.P.  Coefficients  for  Superimposed  Aerofoils. 

G 


82 


AEROPLANE   DESIGN 


course.  Consequently  the  angle  of  attack  of  the  surfaces 
behind  the  main  planes  must  be  reckoned  with  regard  to  the 
actual  direction  of  this  deflected  air  stream.  The  tail  plane 


Angle       of        lnctdet\oe 

FIG.  62. — Lift/Drag  Ratio  for  Superimposed  Aerofoils. 

operates  directly  in  the  downwash  of  the  wings,  and  this  effect 
must  be  carefully  considered  when  the  setting  of  the  tail  plane 
is  being  determined.  Investigations  made  by  Eiffel  and  the 
N.P.L.  upon  this  problem  show  that  the  downward  direction  of 


THE    PROPERTIES    OF   AEROFOILS  83 

the  air  stream  persists  for  some  distance  behind  the  planes,  and 
later  experiments  have  shown  that  the  angle  of  downwash  is 
half  the  angle  of  incidence  of  the  main  planes  measured,  from 
the  angle  of  no  lift. 

Decalage. — The  term  decalage  is  used  to  define  the 
difference  in  the  angle  of  incidence  between  two  aerofoils  of  the 
same  machine.  For  example,  the  upper  plane  of  a  biplane  may 
be  set  at  a  different  angle  to  the  lower  plane  ;  or  the  upper  and 
lower  planes  of  a  triplane  may  be  set  at  different  angles  to  the 
middle  plane  ;  and,  again,  the  setting  of  the  tail  plane  may  be 
different  from  the  inclination  of  the  main  planes.  Decalage  is 
illustrated  in  Fig.  63. 

It  has  been  found  experimentally  that  the  effect  of  setting 


Ineidtnce  of  Ltircr  Pi* 


CXe»lnq«   of  Tail  Ptgx 


FIG.  63. — Decalage. 

the  upper  surface  of  a  staggered  biplane  at  about  2°  less 
incidence  than  the  lower  surface  results  in  a  pronounced  increase 
in  the  lift,  and  a  small  increase  in  the  L/D  ratio  over  any  other 
arrangement.  Such  a  result,  however,  is  modified  when  different 
wing  sections  are  used  ;  and  there  is  room  for  considerable 
investigation  into  the  problem  of  best  wing  combination, 
considering  gap,  stagger,  decalage  and  interference  effects. 
Decalage  has  the  further  advantage  of  reducing  the  instability  of 
the  C.P.  curve,  and  even  of  stabilising  the  C.P.  travel,  if  the 
angle  between  the  surfaces  is  sufficiently  great.  Unfortunately 
this  results  in  a  loss  in  the  aerodynamic  efficiency  of  the 
system. 

Stagger. — When  the  upper  plane  is  set  ahead  of  or  behind 
the  lower  plane  in  the  biplane  or  triplane  arrangement  the 
planes  are  said  to  be  staggered,  the  amount  of  stagger  being  the 
horizontal  distance  between  a  vertical  dropped  from  the  leading 
edge  of  the  upper  plane  and  the  leading  edge  of  the  lower 
plane  or  planes.  Positive  and  negative  stagger  is  illustrated  in 
Fig.  64.  In  certain  machines  stagger  has  been  adopted  in  order 


84 


AEROPLANE    DESIGN 


to  give  increased  visibility,  but  the  constructional  difficulties 
are  naturally  greater  than  in  the  no-stagger  arrangement. 
Positive  stagger  leads  to  a  slightly  increased  efficiency  over  the 
no-stagger  position,  but  this  increase  only  becomes  apparent 
when  the  stagger  is  about  half  the  chord.  Under  these  con- 


No      Sta09«r 


>* 


FIG.  64. — Stagger. 

ditions  there  is  a  gain  in. the  lift  and  the  L/D  of  about  5%. 
Negative  stagger,  so  far  as  present  investigations  go,  would 
appear  to  be  approximately  of  the  same  efficiency  as  the  no- 
stagger  arrangement. 

From    the   designer's   standpoint,    the   question    of   stagger 
must  be  treated  in  conjunction  with  the  amount  of  gap  desirable, 


J*"" 

""-*£* 

/ 

^"Vy. 

^.S' 

/ 

\ 

,/ 

>^ 

10* 

1 

V' 

/ 

\ 

Mf* 

/ 

/ 

/ 

j 

6* 

f 

1 

ffl 

2 

/*' 

&4t 

so* 

•I 

,  ••,.  '• 

t 

y 

»         ( 

> 

Uf|--Ky 

FIG.  65. 

since  stagger  can  be  used  to  advantage  when  the  gap  is  small 
in  order  to  counteract  the  loss  in  aerodynamical  efficiency  due 
to  interference. 


The    Choice    of    an    Aerofoil.  —  Before    concluding    this 
chapter   a   short   space   can    profitably  be   devoted    to   a  brief 


THE    PROPERTIES   OF   AEROFOILS         %         85 

outline  of  one  or  two  simple  methods  of  selecting  an  aerofoil 
which  will  be  suitable  for  a  wing  section  for  various  specific 
purposes.  Curves  of  lift,  drag,  and  L/D,  and  travel  of  the  C.P., 
for  some  of  the  most  successful  aerofoils  yet  evolved,  will  be 
given  at  the  end  of  this  chapter  ;  and  a  careful  examination  of 
these  curves,  together  with  the  following  matter,  will  enable  the 
choice  of  the  most  suitable  aerofoil  for  certain  definite  conditions 
to  be  made. 

Having  drawn  the  curves  of  lift  and  L/D  ratio  for  an  aerofoil 
as  shown  in  Fig.  40,  a  further  curve  can  be  constructed  by 
eliminating  the  angle  of  incidence.  This  is  shown  in  Fig.  65. 
For  the  purposes  of  preliminary  design  work  and  for  comparison 
this  method  of  graphing  wind-tunnel  results  is  much  more 
convenient  than  that  shown  in  Fig.  40,  as  the  angle  of  incidence 
is  not  of  importance  until  the  question  of  the  actual  position  of 
the  wing  arises.  The  method  of  obtaining  such  curves  is 
obvious  from  the  figure,  the  corresponding  value  of  the  lift,  and 
the  L/D  being  taken  at  each  angle  of  incidence. 

A  further  method  of  plotting  results  useful  for  preliminary 
design  work  is  obtained  by  remembering  that  the  landing  speed 
of  a  machine  depends  upon  the  maximum  lift  coefficient  of  the 
section  used.  Thus,  if  V  be  the  landing  speed  and  K  the 
maximum  lift  coefficient, 

W  =  KP  A 


Also  for  any  speed  of  horizontal  flight  V' 
W  =  K'pAV'2/T 

where  K'  is  the  lift  coefficient  at  the  corresponding  angle  of 
incidence.  Hence,  equating  these  two  expressions  we  have 

KV2  =  K'V'2 
or     V  -  V  (|>)4      '.  ..........  Formula  16 

By  means  of  Formula  16  the  speed  at  various  angles  of  inci- 
dence can  be  determined  if  the  corresponding  values  of  the  lift 
coefficients  are  known.  For  example,  if  we  take  the  R.A.F. 
6  aerofoil,  we  see  from  Fig.  65  that  the  maximum  lift  coefficient 
is  '6  approx.,  so  that  if  a  landing  speed  of  45  m.p.h.  is  desired, 
we  have  from  Formula  16 

*;-•«©' 

so  that  by  substitution  of  K'  (the  lift  coefficient  at  any  other 
angle  of  incidence),  the  speed  at  that  angle  can  be  obtained. 


86 


AEROPLANE   DESIGN 


Formula  16  can  also  be  put  into  the  form 

y_ 

v 

that  is,  the  ratio  of  the  landing  speed  to  any  other  speed  may 
be  expressed  in  terms  of  the  lift  coefficients  of  the  aerofoil 
section.  Combining  this  ratio  with  the  L/D  ratio  for  the  aero- 
foil, a  further  graph  can  be  obtained  as  shown  in  Fig.  66,  the 
calculations  for  which  are  arranged  in  tabular  form  below. 


A 

~X 

V 

^ 

^ 

S- 

A 

3 

/ 

' 

16*: 

7 

A 

Values  of  & 


FIG.  66. 


S 
K' 

(V) 

V 
V 


o 
074 

16400 

128 


2 
-173 

7030 

84 


TABLE  XXL—  CALCULATIONS  OF  V/V. 

8° 
-423 

2880 

537 


4° 

-275 

4420 

66-5 


6° 
-354 

3440 

587 


10° 
'496 

2450 

49-5 


12° 
'564 

2l6o 

46-5 


14 
'593 

2050 

45-3 


f77        "35      '535      '677     '7^7     '839      '9*       '9^8      '994 


16°  18° 

•600  -55 

2O2O  2210 

45  47 

i  '96 


10*9      14*3     14*1      12*9     ii'4     io'4      9*3        6^9       4*1 


From  this  curve  the  most  efficient  speed  and  the  value  of  the 
L/D  ratio  for  the  wings  at  the  maximum  flight  speed  required 
can  at  once  be  determined.  For  example,  since  the  maxi- 
mum L/D  gives  the  value  of  V/V  as  72,  the  most  efficient  flying 
speed  so  far  as  the  wings  are  concerned  =  45/72  =  62*5  m.p.h. 
Also  if  a  maximum  speed  of  100  m.p.h.  is  required,  the  value  of 
V/V'  is  then  =  45/100  =  "45,  and  for  this  value  the  curve  shows 


THE   PROPERTIES   OF   AEROFOILS  87 

that  the  L/D  ratio  is  only  just  over  8,  so  that  this  section  is  not 
suitable  for  a  high-speed  machine. 

The  L/D  ratio  for  the  complete  machine  can  only  be  deter- 
mined when  the  drag  of  the  body  has  been  added  to  that  of  the 
wings,  but  the  curve  shown  in  Fig.  66  will  ^indicate  at  a  very- 
early  stage  in  the  design  whether  the  wing  section  chosen  is 
suitable  for  the  desired  purpose.  It  is  very  convenient  for 
design  purposes  to  graph  a  large  number  of  tests  upon  sections 
in  this  manner  and  to  file  them  for  future  reference,  indicating 
upon  each  graph  the  name  of  the  section  and  the  source  from 
which  the  figures  were  obtained.  All  the  curves  should  be 
drawn  to  the  same  scale  upon  good  quality  tracing  linen,  so 
that  one  curve  can  be  readily  compared  with  another  for  minute 
differences  by  superposition. 

The  curve  in  Fig.  66  also  shows  that  a  machine  can  only  fly 
horizontally  at  a  high  speed  if  the  angle  of  incidence  of  the 
wings  is  much  smaller  than  that  for  which  the  L/D  ratio  is 
a  maximum.  From  what  has  already  been  said,  it  follows  that 
for  a  machine  to  have  a  large  range  of  flying  speeds  the  wings 
must  possess  the  following  characteristics  : — 

1.  A  large  value  for  the  maximum  lift  coefficient. 

2.  For  small  angles  of  incidence  the  value  of  the  lift  coefficient 

may  be  small,  but  the  corresponding  value  of  the  L/D 
ratio  must  be  large. 

3.  The  section  should  have  a  large  value  of  the  maximum 

L/D,  and  the  ratio  of  the  maximum  lift  coefficient  to 
the  lift  coefficient  at  the  maximum  L/D  must  be  large. 

Practical  considerations  necessitate  that  the  movement  of  the 
centre  of  pressure  over  the  range  of  flying  angles  should  be  small 
in  order  to  obtain  longitudinal  stability,  and  from  a  construc- 
tional point  of  view  the  depth  of  the  aerofoil  section  must  be 
such  that  an  economical  spar  section  can  be  adopted. 

Units. — The  units  which  are  used  in  the  published  results 
of  aerodynamic  research  work  in  Great  Britain  are  known  as 
absolute  units,  or  absolute  coefficients.  From  Formulae  13 
and  14  we  have 

Lift  =  Ky  £  A  V2 
g 

whence     Ky  =  Absolute  lift  coefficient 


Lift  .          ,  , 
Formula  13  (a) 


g 


88  AEROPLANE   DESIGN 

and        Drag  =  KX^AV2 

& 

whence     Kx  =  Absolute  drag  coefficient 

Formula  14  (a) 

a  A  v8 

Similarly  the  moment  of  an  aerofoil 

=  Mc  —  A  V2  ^       Formula  17 

where  Mc  represents  the  absolute  moment  coefficient  and  b  repre- 
sents the  breadth  of  the  wing  chord. 

It  is  desirable  that  all  measurements  should  be  made  in 
terms  of  the  same  units,  whether  the  C.G.S.  or  the  F.P.S.  system 
is  employed.  For  example,  in  the 'C.G.S.  system,  metres,  metres 
per  second,  kilograms,  square  metres,  etc.,  should  be  used  ;  and 
in  the  F.P.S.  system,  feet,  feet  per  second,  Ibs.,  square  feet,  etc., 
should  be  used. 

In  order  to  obtain  actual  values  from  the  absolute  coefficients, 
the  absolute  values,  which  are  of  course  independent  of  any 
system  of  units,  must  be  multiplied  by  the  remainder  of  the 
expression  shown  in  Formulae  13,  14,  17  expressed  in  appropriate 
units. 

The  value  of  £  in  F.P.S.  units  for  air  at  sea-level  at  a  tem- 

g 

perature  of  15°  C.,  and  at  normal  pressure,  is  '00237,  while  in 
the  C.G.S.  system  under  the  same  conditions  it  is  '125.  Con- 
sequently in  the  F.P.S.  system,  if  we  wish  to  convert  absolute 
values  of  the  lift  coefficient  to  actual  values,  we  have 

absolute  value  x   -00237   x  area  in  sq.  ft.   x  square  of  velocity 
in  feet  per  second 

while  in  the  C.G.S.  system  we  have 

absolute  value  x  '125   x  area  in  sq.  ms.   x  square  of  velocity 
in  ms.  per  second 

The  Law  of  Similitude. — Since  the  lift,  drag,  and  L/D 
coefficients  of  an  aerofoil  vary  with  the  speed,  as  shown  by 
Fig.  39,  it  is  not  possible  to  pass  directly  from  model  tests  to 
full-size  machines.  Lord  Rayleigh  called  attention  to  this  fact, 
and  pointed  out  that  the  most  general  relationship  between  the 
quantities  connected  with  aerodynamics  could  be  expressed  in 
the  form 


F  =  ^V2L2/—      Formula  1 8 

g 


THE    PROPERTIES   OF   AEROFOILS  89 

where  v  represents  the  kinematic  viscosity  of  the  air.     For  the 

V  L 

condition  of  dynamic  similarity  to  be  satisfied  -    -  must  be  the 

same  for  the  model  test  and  the  full-scale  machine.  With  a 
four-foot  wind  tunnel  the  scale  of  the  models  tested  is  generally 
about  one-twelfth.  Consequently,  since  the  kinematic  viscosity 
may  be  regarded  as  constant  for  the  two  cases,  it  would  be 
necessary,  in  order  to  preserve  dynamic  similarity,  to  test  the 
models  at  a  speed  of  1000  m.p.h.  .  This  is  obviously  impossible, 
and  it  has  therefore  been  suggested  that  a  correction  factor, 
known  as  the  V  L  correction,  should  be  applied  to  the  results 
of  model  tests  before  they  are  applied  to  full-scale  machines. 
The  N.P.L.  and  others  have  investigated  this  question,  but  the 
results  so  far  obtained  are  not  conclusive.  Although  increase 
of  L/D  ratio  was  obtained  with  increase  of  speed,  as  shown  in 
Fig.  39,  this  increase  was  not  maintained,  and  a  maximum  value 
would  appear  to  be  reached  with  increase  of  speed.  The  latest 
work  on  the  subject  seems  to  suggest  a  motion  in  which  the 
resistance  decreases  with  an  increase  of  viscosity,  and  Mr.  Bair- 
stow  suggests  that  an  increase  of  viscosity  may  render  this 
possible  by  making  a  different  type  of  motion  stable,  and  so 
reducing  the  turbulence  of  flow. 

Considering  all  the  available  data  upon  this  point,  it  is 
apparent  that  it  is  at  least  on  the  safe  side  to  test  a  model  in 
the  wind  tunnel  at  a  speed  of  from  twenty  to  thirty  miles 
per  hour  (30  to  44  feet  per  second),  and  then  to  apply  the 
results  so  obtained  without  correction  to  full-scale  design.  This 
subject  is  essentially  one  upon  which  the  designer  must  keep 
an  open  mind  and  modify  his  views  as  shown  to  be  necessary 
by  the  results  of  the  latest  published  researches  into  this  subject, 
and  by  the  results  of  his  own  applications  of  model  figures 
to  full-scale  design.  In  this  connection  the  findings  of  a  special 
committee  appointed  to  consider  this  matter  are  of  interest. 
They  are  : 

1.  For  the  purpose  of  biplane  design  model  aerofoils  must 

be  tested  as  biplanes,  and  for  monoplane  design  as 
monoplanes.  The  more  closely  the  model  wing  tested 
represents  that  used  on  the  full-scale  machine,  the 
more  reliable  will  the  results  be. 

2.  Due  allowance  must  be  made  for  scale  effect  on  parts 

where  it  is  known.  In  the  case  of  struts,  wires,  etc., 
the  scale  effect  is  known  to  be  large,  but  these  parts 
can  be  tested  under  conditions  corresponding  with 
those  which  obtain  on  the  full-scale  machine. 


90  AEROPLANE   DESIGN 

3.  The  resistances  of  the  various  parts  taken  separately  may 

be  added  together  to  give  the  resistance  of  the  com- 
plete aeroplane  with  good  accuracy,  provided  the  parts 
which  consist  of  a  number  of  separate  small  pieces 
(e.g.)  the  under-carriage)  are  tested  as  a  complete  unit. 

4.  Model   tests   form    an   important   and   valuable  guide   in 

aeroplane  design.  When  employed  for  the  determina- 
tion of  absolute  values  of  resistance,  they  must  be  used 
with  discrimination  and  a  full  realisation  of  the 
modifications  which  may  arise  owing  to  interference 
and  scale  effect. 

Wing  Sections. —  The  dimensions  and  aerodynamic  charac- 
teristics of  some  highly  successful  wing  sections  are  shown  in 
Figs.  67-76.  All  of  these  sections  have  been  tested  in  actual 
aeroplanes  and  have  proved  themselves  efficient  in  flight.  They 
can  therefore  be  confidently  recommended  for  design  purposes, 
the  section  for  any  particular  machine  being  selected  as  explained 
in  this  chapter. 


THE    PROPERTIES    OF   AEROFOILS 


o-i     r  o-i  -*-  o-i  — «r  OH  -~o-i  -"  CM—*-  o-i  -*-  o-i— -  o-i 


10 


FIG.  67. — Wing  Section  No.  i. 


AEROPLANE    DESIGN 


8'  12"  IG°  20 


FIG.  68.— Wing  Section  No.  2. 


THE   PROPERTIES   OF   AEROFOILS  93 


[  osf  os-K  o-i  —f-  01  H*-  o-i  -+-  01  — t-  01  -4-  o  i  — j~  0 


Angle       of      Incidervce 


FIG.  69. — Wing  Section  No.  3. 


94 


AEROPLANE    DESIGN 


t   i    t    i    i 


0-6 


06 


r\ 


o  V  B*  12' 

Angle     ot    Incidence 


FIG.  70. — Wing  Section  No.  4. 


THE    PROPERTIES    OF   AEROFOILS 


95 


16°  20° 


FIG.  71. — Wing  Section  No.  5. 


96 


AEROPLANE    DESIGN 


Angle      of       Incidence. 


FIG.  72. — Wing  Section  No.  6. 


THE    PROPERTIES    OF   AEROFOILS 


97 


10 

20* 


FIG.  73. — Wing  Section  No.  7. 


H 


98 


AEROPLANE    DESIGN 


-4-  o-'  — j-oi  -4-0-1— | 


FIG.  74.— Wing  Section  No.  8. 


THE    PROPERTIES   OF   AEROFOILS 


99 


16 


14 


12 


10 


t''1f"~1r"s 
9          9         9» 

TITTTTTTT^ 


20' 


FIG.  75. — Wing  Section  No.  9. 


IOO 


AEROPLANE   DESIGN 


FIG.  76. — Wing  Section  No.  10. 


CHAPTER   IV. 
STRESSES  AND  STRAINS  IN  AEROPLANE  COMPONENTS. 

Moments  of  Inertia. — The  product  of  an  area  and  its 
distance  from  a  given  axis  is  termed  the  moment  of  that  area 
about  the  given  axis.  Thus  in  Fig.  77,  if  d&  represent  a  small 
element  of  area  of  the  surface  s  and  y  and  x,  the  perpendicular 
distances  of  this  area  from  the  axes  of  x  and  y  respectively,  then 

d  A  .y  =  the  moment  of  dA  with  reference  to  the  axis  of  x 
dA  .  x  =  the  moment  of  dA  with  reference  to  the  axis  of  y 


FIG.  77. — First  Moment  of  Area.       FIG.  78. — Second  Moment  of  Area. 

The  total  moment  of  the  surface  s  about  these  axes  is  the  sum 
of  such  elements  as  d  A  multiplied  by  the  distance  of  each  of 
these  elements  from  the  required  axis,  or 

Moment  of  s  about  the  axis  ox  =  ^dA.y    Formula  19 

Moment  of  s  about  the  axis  o  Y  =  ZdA.x  Formula  20 

For  many  purposes  the  area  of  the  surface  S  may  be  regarded 
as  concentrated  at  a  single  point  C,  the  position  of  the  point  C 
with  reference  to  any  axis  being  obtained  from  the  relations 


and 

A  x  y  = 
A  x  x  = 

VdA.y 

or 

y  — 

A 

^dA.x 

A 

Formula  21 


Formula  22 


102  AEROPLANE   DESIGN 

where  A  represents  the  total  area  of  the  surface  S,  that  is  the 
sum  of  such  elements  as  d  A,  that  is  S  d  A. 

The  intersection  of  two  such  lines  as  A  c  and  B  c  in  Fig.  77, 
obtained  by  means  of  these  two  formulae,  gives  the  position  of 
the  centroid  c,  which  for  a  homogeneous  lamina  corresponds  to 
the  centre  of  gravity. 

The  product  of  an  area  by  the  square  of  its  distance  from 
a  given  axis  is  termed  the  Moment  of  Inertia  of  the  area  about 
the  given  axis.  Thus  in  Fig.  78,  using  the  same  notation  as  in 
Fig.  77,  we  have 

d  A  .  jy2  =  moment  of  inertia  of  element  d  'A  about  the  axis  of  x 
d  A  .  x*  =  moment  of  inertia  of  element  dA  about  the  axis  of  y 

and  the  total  Moment  of  Inertia  of  the  whole  surface  S  is  the 
sum  of  such  elements  multiplied  by  the  squares  of  their  respec- 
tive distances  from  the  given  axis,  whence 

Moment  of  Inertia  of  s  about  o  x  =  S  d  A  .  y2  =  Ixx     Formula  23 
Moment  of  Inertia  of  s  about  o  Y  =  2  d  A  .  x1  =  IYY     Formula  24 

The  term  '  moment  of  inertia  '  is  somewhat  misleading,  and,  as 
will  be  apparent  from  Figs.  77  and  78,  the  term  *  second  moment  ' 
is  much  more  applicable.  The  term  moment  of  inertia  is,  how- 
ever, in  general  use. 

Now,  in  Fig.  78,  if  K  be  such  a  point  that 

A  x  (yj=  S^A./=  Ixx 
A  x  (X)2  =  S</A.*2  =  IYY 

then  the  point  K  in  Fig.  78  is  analogous  to  the  point  C  in  Fig.  77, 
and  the  distances  y  and  x  are  known  as  the  radii  of  gyration 
of  the  area  A  about  XX  and  YY  respectively.  These  radii  of 
gyration  are  usually  denoted  by  the  symbols  /£x  and  £Y,  so  that 


=  V   % 


Formula  25 


and     /£Y  =  V   —  p         ...............  Formula  26 

A 

Two  very  useful  formulae  connecting  moments  of  inertia 
about  different  axes  are  as  follows  :  — 

i.  PRINCIPLE  OF  PARALLEL  AXES.  —  If  Icx  gives  the  moment 
of  inertia  through  the  centroid  with  reference  to  the  axis  of  x, 
and  ICY  the  moment  of  inertia  with  reference  to  the  axis  of  y,  then 

_2 

Icx  =  Ixx  -  Ajy        .  ...........  Formula  27 

and     ICY  =  IYY  -  AS       ............  Formula  28 


STRESSES  AND  STRAINS  IN  COMPONENTS        103 


2.  THE  POLAR  MOMENT  OF  INERTIA.  —  Knowing  the 
moments  of  inertia  about  two  axes  at  right  angles  to  each 
other  through  the  centroid  as  defined  above,  then  the  polar 
moment  of  inertia  (I),  that  is,  the  moment  of  inertia  about  an 
axis  perpendicular  to  each  of  the  given  axes,  is  given  by  the 
relationship 

I  =  lex  +  ICY        ............  ...  Formula  29 

TABLE  XXII.  —  MOMENTS  OF  INERTIA  —  GEOMETRICAL  SECTIONS. 


Nar^e 


Area 

A 


Morrjet))-  of    IfjerKa 


Radius  of  Qy«.W 


Modulus 


Rectangle 


BH 


BH3 
12 


H2 
12 


BH3 
6 


Hollow 
Rectangle 


BH-bh 


BH3  -  Oh' 


BH3  -  (;h8 


12 


f2(BH-bh) 


eH 


Pierced 


S   '.  ^ 


y^^y 


BfH-h) 


12 


12 


6H 


BH 
2 


BH 
12 


BH 


Circle 


64 


TD3 
32 


Hollo* 
Circle 


64 


Ellipse 


TTBH 


7T  BH3 
64 


*L 

16 


Hollo* 
Ellipse 


64 


f6(BH-6h) 


32  B 


Channel 


or* 


BH-frh 


BH5- 


12 


l2(6H-t»h) 


6H 


104  AEROPLANE    DESIGN 

Table  XXII.  gives  particulars  with  reference  to  the  Moments 
of  Inertia  of  some  common  geometrical  sections.  Of  these,  the 
solid  rectangle,  the  box  (or  hollow  rectangle),  and  the  I  are 
useful  for  the  spars  of  wings  and  fuselage  struts  in  aeronautical 
work.  Unfortunately,  however,  in  aeronautics  many  sections 
are  employed  to  which  the  standard  results  cannot  be  directly 
applied  with  any  degree  of  accuracy.  In  many  such  cases 
various  empirical  formulae  have  been  devised,  but  the  graphical 
construction  about  to  be  described,  and  outlined  in  Fig.  79, 
gives  results  which  are  generally  more  accurate  than  those 
obtained  by  the  use  of  these  formulae,  while  its  use  does  not 
entail  any  advanced  mathematical  knowledge.  Moreover,  if  the 
work  is  arranged  in  tabular  form  as  shown,  and  if  logarithms 
are  employed  for  the  multiplications,  the  labour  involved  is  not 
so  great  as  would  appear  at  first  sight.  In  using  this  method 
it  is  preferable  to  use  decimal  divisions  of  an  inch,  in  order  to 
reduce  the  calculations  after  summation  of  the  columns.  Fig.  79 
shows  the  form  of  an  interplane  strut  of  a  fineness  ratio  of 
3'5  :  i,  the  Moment  of  Inertia  of  which  is  required  about  both 
axes. 

Taking  the  line  x'  x'  as  the  axis  of  reference,  the  table  shown 
in  Fig.  79  is  prepared.  In  this  example  a  unit  of  "05"  has  been 
taken.  The  strut  is  next  divided  into  any  number  of  equal 
parts  by  lines  drawn  parallel  to  the  axis  of  reference.  In  the 
example  shown  these  lines  were  taken  *i"  apart.  The  mid- 
ordinate  of  each  of  these  sections  is  then  inserted  as  shown  by 
the  lines  i-i,  2-2,  3-3,  4-4,  &c.  The  table  shown  to  the  right  is 
next  drawn  up  and  the  headings  inserted.  The  first  column, 
headed  'jj>,'  represents  the  distance  from  the  line  of  reference 
x'x'  of  the  mid-ordiriate  of  each  of  the  sections  into  which  the 
strut  has  been  divided.  Since  the  strut  is  7"  long,  was  divided 
by  lines  *i"  apart,  and  since  -05"  has  been  adopted  as  the  unit, 
the  figures  in  the  first  column  (y)  will  be  the  odd  numbers 
commencing  with  i  and  running  up  to  139. 

The  second  column,  headed  '.ar/  shows  the  breadth  of  each 
of  the  mid-ordinates  whose  distance  from  the  line  of  reference  has 
been  given  in  the  first  column.  A  diagonal  scale  can  easily  be 
constructed  for  reading  off  these  lengths  to  any  required  degree 
of  accuracy, 

Column  three,  headed  ' a'  represents  the  area  of  each  of  the 
sections,  and  is  obtained  from  column  two  by  multiplying  each 
breadth  by  the  depth  of  the  section.  Since,  in  the  example,  the 
depth  of  each  section  is  constant,  and  equal  to  two  units,  column 
three  is  obtained  from  column  two  by  multiplying  by  two.  The 
total  of  column  three  gives  %  a,  that  is,  the  area  of  the  section 


STRESSES  AND  STRAINS  IN  COMPONENTS        105 

shown  in  terms  of  the  unit  employed.  To  obtain  the  area  in 
square  inches,  we  must  therefore  divide  by  the  square  of  the 
unit,  that  is  by  400,  whence  the  area  of  the  section  is  equal  to 
lO'Oi  square  inches,  as  shown.  The  empirical  formula  for 
finding  the  area  of  the  section  illustrated  is 

A  =  2-5  /4 
whence  A  =  10  sq.  ins. 

so  that  the  agreement  is  very  close. 

The  fourth  column,  headed  '  ay]  gives  the  first  moment  of 
each  section  about  the  axis  of  reference  X'X'.  Its  total  therefore 
represents  ^ay,  and  by  dividing  this  total  by  £#,  we  obtain 
the  position  of  the  centroid  of  the  section  with  regard  to  the 
line  X'X7.  As  shown,  this  distance  is  S'8/'. 

Column  five  is  obtained  by  multiplying  column  four  by  ' yl 
and  gives  the  second  moment,  or  moment  of  inertia,  of  the 
sections  with  reference  to  the  axis  X'X'.  Dividing  the  sum 
%  ay1  of  this  column  by  the  fourth  power  of  the  unit  used, 
gives  the  moment  of  inertia  of  the  whole  section  about  X'X' 
in  inch4  units.  The  result,  as  shown  in  Fig.  79,  is  178*18. 
Applying  the  principle  of  Parallel  Axes  to  find  the  moment  of 
inertia  about  the  line  through  the  centroid  parallel  to  X'X',  the 
figure  29*26  is  obtained,  as  shown. 

The  moment  of  inertia  about  an  axis  at  right  angles  to  X'X' 
can  be  found  in  exactly  the  same  manner.  Since,  however,  the 
section  is  symmetrical  about  Y  V,  it  is  only  necessary  to  consider 
one-half  of  the  section,  and  to  multiply  the  results  obtained  by 
two,  in  order  to  obtain  the  correct  results  for  the  complete 
section.  As  will  be  seen  from  Fig.  80,  the  moment  of  inertia  for 
the  section  about  Y  Y  =  2-35  inch4  units.  The  empirical  formula 
for  finding  the  moment  of  inertia  of  this  section  about  Y  Y  is 

M.I.  =  -15  /* 

=  2*4  inch4  units. 

The  accuracy  obtained  in  Figs.  79  and  80  is  far  greater  than 
is  generally  required  in  practical  work,  since  a  wooden  strut 
cannot  be  made  so  accurately  as  these  figures  show,  and  even  if 
made  so  accurately  would  not  retain  its  accuracy  unless  fully 
protected  from  atmospheric  effects.  Consequently  the  labour 
involved  in  preparing  a  table  such  as  is  shown  in  Fig.  79  can  be 
considerably  reduced  by  taking  the  distance  apart  of  the  sections 
•2"  instead  of  *i",  since  the  form  of  the  section  with  reference  to 
the  axis  X'X'  does  not  change  very  rapidly.  Since  the  form  of 
the  section  changes  fairly  rapidly  with  reference  to  the  axis  Y  Y, 
it  is  not  advisable  to  increase  the  distances  apart  of  the  sections 


FIG.  79.  —  Moment  of  Inertia  of  Streamline 
Section  about  Axis  XX. 

Area    of  Sechor? 


DisVaTtce  of  Line   tVough  Cent-rcid   fro«t?  X'X 


of  IrrerVia 


-  gay*  _    28509652-1 
20*  20*- 

«       178-16   inch4  unfa 


Moment'  of  IgerHa     atouV       XX 

--U     -'Ay3 

*  178-18  -     149-92 

=  29-  26     mcfc^  unite 


X' 

Y 

y      x 

a         ay 

ay* 

i    ...     5*8 

ir6    ...     11*6 

11*6 

3    •..     7'6 

15-2    ...     45-6 

136-8 

5    ...     8-4 

16*8    ...      84-0 

420*0 

7    •..     9'4 

1  8-8    ...     131-6 

921*2 

9    ...    10*8 

21*6      ...       194*4 

1749-6 

ii    ...    11-8 

23-6    ...     259-6 

2855*6 

13    ...    12-8 

25-6    ...     332-8 

4326-4 

15    ...    13*8 

27-6    ...     414*0 

6210*0 

17    ...    15*0 

30*0    ...     510-0 

86700 

19    ...    16-0 

32*0    ...     608*0 

11552-0 

21    ...    17-2 

34-0    ...     722-4 

15170-1 

23    ...    18-2 

36-4    ...     837-2 

19255-6 

25    ...    19-4 

38*8    ...     970*0 

24250-0 

27      ...      20'0 

40*0    ...    1080*0 

29160-0 

29      ...      21-2 

42*4    ...    1229-6 

35658*4 

31      ...      22'2 

44-4    ...    1376*4 

42668-4 

33    ...    23-2 

46*4    ...    1531*2 

50529-6 

35    ...    24-4 

48-8    ...    1708-0 

59780-0 

37    .-    25-0 

50-0    ...    1850-0 

'  68450-0 

39    ...    26-0 

52-0    ...    2028*0 

79092-0 

FIG.  79. — Moment  of  Inertia  of  Streamline  Section  (continued}. 


y 

X 

a 

ay 

ay* 

41 

27-0 

54-0 

2214*0 

90774-0 

43 

28-0 

56*0 

2408*0 

103644-0 

45 

29'0 

58-0 

2010*0 

117450-0 

47 

29-4 

58-8 

2763-6 

129889-2 

49 

30-4 

60-8 

2979-2 

145980-8 

51 

31-2 

62  '4 

3182-4 

162302*4 

53 

32-0 

64*0 

3392-0 

179776*0 

55 

32-6 

652 

3586-0 

197230*0 

57 

33-6 

67-2 

3830-4 

218332-8 

59 

34'4 

68-8 

4059-2 

239492-8 

61 

35-0 

70  'o 

4270*0 

260470*0 

63 

35'6 

71-2 

4485-6 

282592-8 

65 

36-2 

72-4 

4706-0 

305890-0 

67 

36-8 

73'6 

4931*2 

330390*4 

69 

37'4 

74-8 

5161-2 

356122*8 

71 

38-0 

76-0 

5396-0 

383116*0 

73 

38-4 

76-8 

5606-4 

409267-2 

75 

38-8 

77'6 

5820*0 

436500*0 

77 

39-2 

78-4 

6036-8 

464833-6 

79 

39-4 

78-8 

6225-2. 

491790-8 

81 

39'5 

79-0 

6399-0 

518319-0 

83 

39"6 

79-2 

6573-6 

545608-8 

85 

397 

79"4 

6749-0 

573665-0 

87 

39'8 

79-6 

6925-2 

002492-4 

89 

40*0 

80-0 

<..    7120-0 

.  633680-0 

91 

40*0 

80-0 

7280-0 

662480*0 

93 

40*0 

80-0 

7440-0 

691920*0 

95 

400 

80-0 

7600-0 

722000-0 

97 

40*0 

80-0 

7760-0. 

752720-0 

99 

39'8 

79-6 

7880-4 

780159*6 

101 

39"6 

79-2 

7999'2 

807919*2 

103 

39'o 

78-0 

8034-0 

827502-0 

105 

38-4 

76-8 

8064*0 

846720-0 

107 

38-0 

76*0 

8132-0 

870124*0 

109 

37-6 

75*2 

8196-8 

893451*2 

in 

37'o 

74-0 

8214*0 

911754*0 

113 

36-6 

72-2 

8271*6 

934690*8 

115 

35*4 

70-8 

8142*0 

936330-0 

117 

34'6 

69*2 

8096-4 

947278-8 

119 

33'4 

66-8 

7949'2 

945954-8 

121 

32-6 

65-2 

7889-2 

954593'2 

123 

3i'o 

62-0 

7626-0 

937998*0 

125 

29*6 

59-2 

7400*0 

925000-0 

127 

27-6 

55-2 

7010-4 

890320*8 

129 

25-6 

51-2 

6604-8 

852019*2 

131 

23-2 

46-4 

6078*4 

796270*4 

133 

20-4 

40-8 

5426-4 

721711*2 

135 

I7'2 

34'4 

4644*0 

626940-0 

137 

I2'2 

24-4 

3342-8 

457963-6 

139 

4'6 

9-2 

1278-8 

177753*2 

4005*2 


309724*8 


28509652*1 


io8 


AEROPLANE   DESIGN 


parallel  to  this  axis,  and  as  will  be  seen  from  Fig.  80,  the  labour 
involved  in  this  case  is  not  very  considerable. 


y 

X 

a 

ay 

ay7 

•? 

f  39-9 

279-8 

279-8 

279-8 

3 

138-0 

27«-0 

828-0 

2484-0 

5 

139-9 

259-8 

1299-0 

6495-0 

7 

120-8 

24  1-6 

169!  -2 

1  1836.4 

9 

1  r  0  8 

22  1-6 

1994-4 

I7949-6 

1  1 

103-7 

2O7-4 

2281  -4 

35O95-4 

1  3 

a?'* 

174-8 

2272-4 

2-9541-2 

1  5 

76-0 

152-0 

2280-0 

34200-0 

17 

58-2 

H6-4 

1976-6 

33779-6 

1  9 

360 

72-0 

1  366-0 

25992-0 

2001,  -4 

16273-0 

f87655-0 

.   187655 

20* 
-     2-35    incV>4« 


FIG  80. — Moment  of  Inertia  of  Streamline  Section  about  Axis  Y  y. 


Nomograms,  sometimes  called  alignment  charts  in  England, 
can  be  prepared  for  some  of  the  formulae  given  in  Table  XXII. 
and  many  other  formulae  in  use  in  aeronautics,  from  which 
the  value  of  the  moment  of  inertia,  or  other  quantity  for  which 
the  nomogram  has  been  constructed,  can  be  read  off  im- 
mediately within  the  limits  of  the  graduations. 

Fig.  8 1  shows  a  nomogram  constructed  to  give  the  moment 

of  inertia  of  a  rectangle,  that  is  the  quantity  - 

To  use  nomograms  it  is  very  convenient  to  scribe  a  straight 
line  on  the  under  side  of  a  large  celluloid  set  square.  Fig.  Si 
is  then  used  in  this  manner.  Suppose  that  it  is  required  to  find 
the  moment  of  inertia  of  a  rectangle  whose  breadth  is  '6"  and 
whose  depth  is  2" '.  The  line  scribed  on  the  set  square  is  placed 
over  the  '6  graduation  on  the  breadth  scale  and  swung  round 
until  it  is  over  the  2"  mark  on  the  depth  scale.  Where  the  line 
cuts  the  moment  of  inertia  scale  gives  the  answer,  and  as  will  be 
seen  this  gives  the  moment  of  inertia  as  '4  inch4  units.  The 
same  nomogram  can  also  be  used  to  find  the  moment  of  inertia 
of  a  square  placed  either  with  its  axis  parallel  to  or  diagonal  to 
the  line  of  reference,  remembering  that  the  reading  on  the 


STRESSES  AND  STRAINS  IN  COMPONENTS         109 

breadth  scale  must  be  the  same  as  the  reading  on  the  depth 
scale.  It  can  also  be  used  to  find  the  moment  of  inertia  of 
a  hollow  rectangle,  I  beam,  channel,  or  hollow  square,  by 


FIG.  81. — Nomogram  for  determining  the  Moment  of  Inertia 

of  Rectangle,  Square,  Hollow  Rectangle,  Channel 

and  '  I '  Sections. 


finding  the  difference  between  the  moments  for  the  whole  and 
the  missing  portion.  The  following  example  will  help  to  make 
this  clear. 


no  AEROPLANE   DESIGN 

To  find  the  M.I.  of  the  box  section  illustrated  in  Fig.  82  : 

M.I.  of  whole  section      =  -667  from  nomogram. 
M.I.  of  missing  portion  =  -137      „ 

M.I.  of  the  box  section  =  '53  inch*  units. 


FIG.  82. 


Shear  Force  and  Bending  Moment. — To  obtain  a  clear 
idea  of  these  quantities  the  following  definitions  must  be 
carefully  considered  : — 

The  shearing  force  at  any  point  along  the  span  of  a  beam 
is  the  algebraic  sum  of  all  the  perpendicular  forces  acting  on 
the  portion  of  the  beam  to  the  right  OR  to  the  left  of  that  point. 

The  bending  moment  at  any  point  along  the  span  of  a  beam 
is  the  algebraic  sum  of  the  moments  about  that  point  of  all  the 
forces  acting  on  the  portion  of  the  beam  to  the  right  OR  to  the 
left  of  that  point. 

Notice  that  since  the  beam  is  in  equilibrium,  the  algebraic 
sum  of  the  forces  or  the  moments  about  any  point  considered 
on  BOTH  sides  of  the  beam  must  be  zero.  Consequently  the 
same  value  will  be  obtained  for  the  shearing  force  or  the  bending 
moment,  irrespective  of  whether  we  work  from  the  right-hand 
end  or  the  left-hand  end. 

The  cases  illustrated  in  Table  XXIIL,  on  pages  111-13,  are 
of  fundamental  importance,  and  should  be  thoroughly  well  known 
before  any  attempt  is  made  to  apply  the  results  to  aeronautical 
design  work. 


STRESSES  AND  STRAINS  IN  COMPONENTS         in 


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STRESSES  AND  STRAINS  IN  COMPONENTS        113 


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AEROPLANE   DESIGN 


Stresses  in  Beams. — The  assumptions  made  in  the  Theory 
of  Bending  should  always  be  remembered,  because  any  formula 
derived  from  the  Theory  of  Bending  rests  upon  these  assump- 
tions. Consequently,  when  these  assumptions  do  not  hold  good, 
the  resulting  formula  cannot  be  applied  with  safety.  Neglect 
of  this  almost  obvious  precaution  is  the  root  of  practically  all 
cases  of  discrepancy  between  theory  and  practice.  In  order  to 
obtain  a  theory  at  all,  certain  assumptions  have  had  to  be  made. 
Persons  quite  ignorant  of  theory  find  a  formula  in  a  pocket- 
book,  apply  it  to  a  case  (or  cases)  where  the  assumptions  made 
in  deriving  the  formula  do  not  hold  good,  and  when  as  a  result 
failure  occurs,  the  blame  is  laid  at  the  door  of  theory. 

The  chief  assumption  made  in  the  Theory  of  Bending  is 
what  is  known  as  Bernoulli's  Assumption,  namely  : 

1.  Transverse   plane   sections   of  a   beam  which   are*  plane 
before  bending  remain  plane  after  bending. 

The  other  assumptions  made  are — 

2.  That  Hooke's  Law  holds  good. 

3.  That  the  modulus  of  Elasticity  (E)  is  the  same  in  tension 
as  in  compression. 

W 


1 


0      fa' 


FIG.  83.  —  Distribution  of  Longitudinal  Stress  for  I  Section. 

4.  That  the  original  radius  of  curvature  of  the  beam  is  great 
compared  with  the  cross-sectional  dimension  of  the  beam. 

In  simple  bending,  the  external  forces  producing  bending 
form  a  couple  which  is  balanced  by  the  internal  forces  in  the 
fibres  of  the  beam.  These  internal  forces  form  another  couple, 
and  are  the  resultants  of  the  tensile  and  compressive  stresses 
in  the  beam. 

Let  Fig.  83  (a]  represent  a  beam  subjected  to  bending,  whose 
cross-section  is  shown  in  Fig.  83  (b).  Then,  owing  to  the  bend- 
ing moment  M  at  a  cross-section  such  as  c  D,  the  distribution  of 
longitudinal  stress  will  be  as  shown  in  Fig.  83  (c).  The  line  N  A, 
which  passes  through  the  point  of  no  stress,  is  known  as  the 
neutral  axis  of  the  beam.  Since 


/c         J'c 

the  neutral  axis  (N  A)  must  pass  through  the  C.G.  of  the  section.. 


STRESSES  AND  STRAINS  IN  COMPONENTS        115 

Considering  two  transverse  sections  of  a  beam  which  are 
very  close  together,  it  will  be  seen  from  Fig.  86  that,  in  order 
to  fulfil  Bernouilli's  assumption,  after  bending,  the  bounding 
lines  are  no  longer  parallel,  but  that  a  layer  such  as  A  D  has  been 
stretched,  while  a  layer  such  as  B  C  has  been  compressed.  It  is 
obvious  that  there  must  be  an  intermediate  layer,  such  as  M  N, 
which  is  neither  stretched  nor  compressed.  This  layer  is  known 
as  the  neutral  axis  (N.A.). 

Produce  A  B,  CD,  Fig.  86  (b)  to  meet  each  other  in  o,  and 
let  the  angle  contained  by  these  two  lines  contain  a  radians. 
Let  the  radius  of  curvature  of  the  neutral  surface  M  N  =  R,  and 
let  the  height  of  any  layer  such  as  p  Q  from  the  neutral  axis  —  y. 

Then,  from  Fig.  86  (b) 

PJJ  =  (R  +  y)a  = 

M  N  R  a 

and  the  strain  at  a  layer  such  as  P  Q,  is  equal  to 

Extended  length  -  Original  length  =  (R+jy)a-Ra_j 
Original  length  Ra  ~  R 

and  the  longitudinal  tensile  stress  intensity  at  a  distance  y  from 
the  N.A.  within  the  limits  of  elasticity 

=  /'  =  E  x  strain 


These  longitudinal  internal  forces  form  a  couple  which  is 
equal  to  the  bending  moment  at  every  cross  section,  and  us 
known  as  the  Moment  of  Resistance.  Expressing  this  couple 
in  terms  of  the  dimensions  of  the  cross  section  and  equating  to 
the  bending  moment,  we  have 


Combining  these  several  results  in  one  expression,  we  have 

" 


Formula  48 


From  this  equation  we  see  that 


- 

y      R 

The  ratio  I/y  is  known  as  the  modulus  of  the  section.  This 
modulus  is  generally  denoted  by  the  letter  Z,  the  suffix  V  or 
1  c*  being  added  according  as  the  beam  is  in  tension  or  com- 
pression. 


n6  AEROPLANE   DESIGN 

,.  SHEAR  STRESS. — The  complementary  maximum  horizontal 
shear  stress  generally  occurs  at  the  neutral  axis,  the  distribution 
for  any  cross-section  being  given  by  the  expression 


F    /"Y 

q  —  —    /    y ,  b  .  dy Formula  49 

I  bj  v 


where 

q  —  mean  intensity  of  shear  stress  at  a  distance  y  from  the  N.  A. 

F  =  shearing  force  on  the  cross  section  of  the  beam. 

I  =  moment  of  inertia  of  the  cross  section. 

b  =  breadth  of  the  cross  section,  having  a  particular  value  outside 

the  integral,   but  varying   with   the    distance  y  inside  the 

integral. 


FIG.  84.  —  Distribution  of  -Shear  Stress  for  I  Section. 

A  numerical  example  will  make  the  use  of  Formula  49  clear. 
Consider  the  I  section  shown  in  Fig.  84  (a]  : 
1 

At  A,  q  =  o 

6 

^*,*-- 

.'.  for  the  inner  edge,  of  the  flange 


and  for  the  outer  edge  of  web 


At  c,  on  the  neutral  axis, 


+4-5) 


-  .n? 


STRESSES  AND  STRAINS  IN  COMPONENTS        117 

and  since  the  evaluation  of  the  integral  gives  rise  in  each  case 
to^2,  the  curve  of  shear  stress  is  a  parabola,  whence  the  distri- 
bution of  shear  stress  can  be  drawn  from  these  figures  as  shown 


7     86 


--€ 


T/O 


in  Fig.  84  (£).  From  this  figure  it  is  clear  that  the  web  carries 
most  of  the  shear,  and  it  is  usual  on  this  account  to  design  the 
web  on  the  assumption  that  it  carries  all  the  shear,  which  gives 
a  result  on  the  safe  side. 


ii8  AEROPLANE   DESIGN 

Relation  between  Load,  Shear,  Bending  Moment,  Slope, 
and  Deflection.  —  Let  A  B,  Fig.  85,  represent  a  beam  carrying  a 
continuous  load  w  per  unit  of  length,  and  §x  a  length  of  this  beam 
so  small  that  whether  w  is  constant  or  variable,  for  the  distance 
£  x  it  can  be  regarded  as  constant. 

Then  the  forces  acting  upon  this  beam  for  the  section  con- 
sidered are  as  shown  in  Fig.  85. 

Equating  upward  and  downward  vertical  forces,  we  have 

F  +  2  F  =  F  +  w  .  S  # 
whence  &  F  =  w  .  b  x 

—  =  w  ............  Formula  50 

b  X 

that  is,  in  words,  the  rate  of  change  of  the  shearing  force  is 
numerically  equal  to  the  loading;  and  alternatively,  the  integra- 
tion or  summation  of  the  loading  diagram  between  the  correct 
limits  gives  the  shear  force  curve. 

Again,  equating  moments  about  D  for  the  external  forces 
acting  upon  the  section  of  length  S  x>  we  have 


and  since  S  x  represents  a  quantity  of  the  first  order  of  small- 
ness,  products  containing  two  of  these  small  quantities  can  be 
neglected. 

Hence  M  +  F.S#  =  M  +  6M 

or  &  M       ^  T-         i 

-  =  r  ............   Formula  5  1 

o  x 

or  in  words,  the  rate  of  change  of  the  bending  moment  is  equal 
to  the  shearing  force  ;  and  alternatively,  integration  of  the  shear 
force  curve  gives  the  bending  moment  curve. 

The  curvature  of  a  beam  in  accordance  with  the  Theory  of 
Bending  is  given  by  the  relation 


Aa-|3    Formula 

2 


R  (<ly\*~\ 

Li  +  ti)_ 


Neglecting    second    orders    of    smallness    this    expression 
reduces  to 


17      i 

R  ............  Formula  53 


STRESSES  AND  STRAINS  IN  COMPONENTS 

and  for  the  section  &x  shown  in  Fig.  85  we  have  by  the  com- 
bination of  Formulae  51  and  53 

i  d^y       M 

R=    -a?"  II  ^°rmula54 

the  negative  sign  being  inserted  to  make  the  radius  of  curvature 
positive. 

By  adopting  a  suitable  convention  with  regard  to  the  sign 
of  the  bending  moment,  the  last  part  of  Formula  54  may  be 
written 

d'2y     M  /  \ 

J-J  -=£l  ............  Formula  54  (a) 

Integrating  Formula  54  (a)  we  have 

Slope  =  -~  =    I  —  -  dx  ...........   Formula  55 

Ct  OC          J      \2j  L 

Integrating  Formula  55  we  have 

Deflection  =  y    =    I   I  —  dx.dx  ............  Formula  56 

Combining  Formulas  50  and  51  we  have 


which,  combined  with  Formula  54  (a),  gives 

d4  y 
w  =  El—^--        ............  Formula  57 

ax* 

an  expression  which  enables  the  shear,  bending  moment,  slope, 
and  deflection  of  a  beam  to  be  determined  when  the  loading 
is  constant  or  an  integrable  function  of  x. 

For    example,   to    take    Case    8    of    Table   XXIII.    shown 
on  p.   112 

d^y 
Load  =  E  I  —  —  •  =  w 


Shear  =  E  I  -r^  =    w  x     +  A 
dx3 

d'2  y 


Bending  Moment  =  E  I 


But  when  x  =  o,  M  =  o,  .*..  B  =  o 
and  when  x  =  L,  M  =  o 

.-.  AL  =   -  JwL2 

or     A    =   -      w  L 


120  AEROPLANE    DESIGN 

Substituting 
Bending  Moment  =  E  I 


^ 

whence  the  bending  moment  at  the  centre 

=  M  =  J?e/(jL)2  -  JwL(JL) 


Integrating  the  bending  moment  expression 

_     dy      w  x*      w  L  x* 

Slope  =  E  I  — -  = +  C 

ax         6 

Deflection  = 

But  when  x  =  o,  y  =  o,  .*.  D  =  o 
and  when  x  =  L,  y  =  o, 

...  CL  =  ^_^L4 

12  24 

or     C  =  — — 

24 

Substituting 

„  a  w  x*      w  Lx 3      w  L3  x 

Deflection  =  E  I.  y  = +  

24  12  24 

whence  the  deflection  at  the  centre 

=  ^(£L)4  _  ^L(^L)3      w  L3  (I  L) 
-^  24  24  24 


384EI 

It  will  thus  be  seen  that  by  successive  integration  and 
elimination  of  the  constants  of  integration  the  shear,  bending 
moment,  slope,  and  deflection  of  a  beam  can  be  fully  investi- 
gated from  a  knowledge  of  the  loading,  that  is  from  Formula  57. 

In  addition,  from  a  knowledge  of  these  expressions  different 
graphical  methods  can  be  devised  to  suit  particular  cases.  It 
should  also  be  noted  that  the  bending  moment  curve  bears  the 
same  relation  to  the  slope  and  deflection  curves,  as  the  load 
diagram  bears  to  the  shear  and  bending  moment  curves. 

A  very  easy  method  of  summation  which  is  frequently 
useful  in  practice  for  determining  these  quantities  is  the  method 
of  tabular  integration.  The  advantage  of  this  method  is  that 


STRESSES  AND  STRAINS  IN  COMPONENTS        121 


the  actual  arithmetic  of  a  table  such  as  is  shown  below  is 
very  simple,  and  in  addition  the  table  can  be  dispensed  with 
altogether  by  the  use  of  squared  paper  diagrams.  Particular 
attention  must  be  paid  to  scales  if  the  squared  paper  method 
of  application  is  adopted.  This  graphical  adaptation  has  been 
used  in  summing  up  (or  integrating)  the  curves  shown  in  the 
practical  application  of  the  theory  of  the  tapered  strut  in 
Chapter  V.,  and  also  in  dealing  with  the  airscrew  in  Chapter  IX. 
The  tabular  method  of  procedure  will  be  illustrated  by  the 
following  practical  example  : — 

Consider  the  spar  of  a  wing,  8  feet  long,  loaded  uniformly 
with  20  Ibs.  per  foot  run,  and  with  the  equivalent  of 
a  concentrated  load  of  20  Ibs.  at  a  distance  of  5  feet 
from  A,  the  fixed  end. 

The  diagram  of  loading  is  shown  in  Fig.  87. 

TABLE  XXIV. — SHEAR,  BENDING  MOMENT,  SLOPE,  AND  DEFLECTION 
BY  TABULAR  INTEGRATION. 


Distance. 

Load. 

Shear. 

B.M. 

Slope. 

Deflection. 

Jwdx 

fFdx 

flAdx 

fidx 

x 

w 

—  F  4-  A 

—  M+  B 

(A  =  O) 

(B  =  0) 

=  M 

-V+XC«D 

=-.  i  x  E  I 
(C  =  1970) 

+  D 

y  x  El 
(D  =  -  11815) 

O 

O 

O 

0 

-1970 

o 

-  11815*0 

2O 

I 

20 

IO 

5 

-1965 

1967*5 

-   9847*5 

2O 

2 

40 

40 

30 

-1940 

3920-0 

-7895'° 

2O 

60 

3 

20 

80 

90 

95 

-1875 

5827-5 

-5997*5 

20 

4 

IOO 

1  80 

230 

-1740 

7635-0 

-4180*0 

2O 

5 

I2O 

290 

465 

-  J5°5 

9257-5 

.  -2557*5 

20 

6 

I4O 

420 

820 

-  1150 

10585-0 

—  1230*0 

20 

7 

160 

570 

1315 

-ess 

11487*5 

-327*5 

2O 

8 

180 

740 

1970 

-  0 

11815*0 

-0 

122  AEROPLANE    DESIGN 

The  first  column  in  Table  XXIV.  contains  the  distances 
from  the  origin,  which  in  this  case  has  been  selected  at  the  free 
end  B.  The  second  column  contains  the  load  distribution. 
Since  there  is  20  Ibs.  per  foot  run,  20  Ibs.  is  placed  between  each 
pair  of  figures  in  column  I  ;  and  as,  in  addition,  there  is  a  con- 
centrated load  of  20  Ibs.  at  a  distance  of  3  feet  from  B,  20  is 
placed  opposite  the  figure  3  in  the  first  column.  Formula  49 
shows  us  that  to  obtain  the  shear  we  integrate  (that  is,  sum  up) 
the  load..  Column  3  contains  this  summation.  At  a  distance 
of  o  feet  it  is  obvious  that  there  is  no  load,  but  from  o  feet  to 
I  feet  it  is  seen  that  there  is  20  Ibs.,  hence  opposite  figure  I  in 
the  first  column  we  place  20  in  the  third  column.  From  the 
first  to  the  second  foot  there  is  another  20  Ibs.,  which,  added  to 
the  20  already  obtained,  gives  40  as  the  figure  to  be  placed 
opposite  the  second  foot  in  the  third  column.  Now  at  the  third 
foot  there  is  a  concentrated  load  of  20,  which  means  that  there 


FIG.  87. — Load  Diagram. 

will  be  discontinuity  in  the  shear  force  curve  at  that  point. 
Consequently,  in  the  third  column,  we  require  two  figures :  the 
first  figure  showing  the  shear  an  infinitesimal  distance  before 
reaching  the  concentrated  load,  and  the  second  figure  showing 
the  shear  just  as  the  load  is  reached.  Of  course,  in  practice, 
the  mathematical  conception  of  a  load  acting  at  a  point  is 
impossible  of  realisation  ;  and  actually  there  is  a  rounding  off  of 
the  corners  of  the  shear  force  diagram  where  a  load  is  applied, 
the  rounding  off  being  more  or  less  gradual  according  as  the 
load  acts  over  a  longer  or  shorter  distance.  The  remainder  of 
column  3  consists  of  adding  on  20  for  each  foot  length  of 
the  span,  and  is  perfectly  simple.  As  previously  pointed  out, 
when  an  expression  is  integrated  an  arbitrary  constant  appears, 
and  this  constant  should  be  determined  before  proceeding 
further,  if  possible.  On  reference  to  Table  XX II I.,  we  see  that 
the  shear  for  a  cantilever  beam  loaded  as  in  this  example  is 
zero  at  the  free  end.  This  agrees  with  the  value  shown  in 
Table  XXIV.,  so  that  the  constant  of  integration  is  zero,  and 
the  values  shown  in  Table  XXIV.  represent  the  values  of  the 
shear  in  Ibs.  at  each  point  along  the  span. 


STRESSES  AND  STRAINS  IN  COMPONENTS        123 

Integration  of  column  3  gives  the  bending  moment.  The 
process  consists  of  finding  the  area  of  the  shear  force  curve 
above  each  foot  length  of  the  span,  and  adding  this  area 
to  the  result  already  obtained.  The  area  for  the  first  foot 
=  i(p  +  20)  x  I  =  10,  for  the  second  foot  =  J  (20  +  40)  x  I  =  30. 
Adding  to  the  bending  moment  already  obtained  for  the  first 
foot  the  bending  moment  at  the  second  foot  =  40. 

For  the  third  foot  we  have  area         =  J  (40  +  60)  x  i  =    50 

whence  bending  moment  at  the  third  foot    =  40  +  50  =  90. 
Area  for  the  fourth  foot          =  J  (80  +  100)  x  i  =    90 

whence  bending  moment  at  the  fourth  foot  =  90  +  90  =  180. 
Area  for  the  fifth  foot =  £(ioo+ 120)  x  i  =  no 

whence  bending  moment  at  the  fifth  foot     =  180+110  =  290. 
Area  for  the  sixth  foot  =  J  (120+  140)  x  i  =  130 

whence  bending  moment  at  the  sixth  foot    =  290+  130  =  420. 
Area  for  the  seventh  foot        =  ^(140+  160)  x  i  =  150 

whence  bending  moment  at  the  seventh  foot  =  420  +  150  =  570. 
Area  for  the  eighth  foot          =  J(i6o+ 180)  x  i  =  170 

whence  bending  moment  at  the  eighth  foot  =  570+  170  =  740. 

It  now  remains  to  eliminate  the  constant  of  integration.  At 
the  free  end  B  the  bending  moment  must  be  zero,  therefore  the 
constant  of  integration  is  zero,  since  the  bending  moment  at 
that  point  is  already  zero. 

Integration  of  the  bending  moment  curve  gives  the  slope,  so 
column  5  is  obtained  from  column  4  in  exactly  the  same  way 
that  column  4  was  obtained  from  column  3.  To  eliminate  the 
constant  of  integration  we  notice  that  the  slope  must  be  zero  at 
the  fixed  end  A.  Hence  the  constant  of  integration  is  —  1970 
and  column  6,  which  gives  the  slope  multiplied  by  El,  is 
obtained  by  subtracting  1970  from  column  5. 

Integration  of  the  slope  gives  the  deflection,  so  column  6  is 
summed  in  exactly  the  same  way  as  the  previous  columns.  To 
eliminate  the  constant  of  integration  we  notice  that  the  deflec- 
tion is  zero  at  the  fixed  end  A.  Consequently  the  constant  of 
integration  must  be  —  11815,  and  column  8,  which  gives  the 
deflection  multiplied  by  E  I,  is  obtained  from  column  7  by 
subtraction  of  this  constant. 

Struts. — The  use  of  struts  enters  very  largely  into  aeroplane 
construction,  hence  it  is  important  that  the  theory  underlying 
the  formulae  employed  in  their  design  should  be  clearly  under- 
stood and  appreciated.  The  classical  theory  is  due  to  Euler, 


124 


AEROPLANE   DESIGN 


whose  theory  depends  upon  Formula  53.  This  formula,  as  we 
have  just  seen,  rests  upon  the  assumptions  made  in  the  theory 
of  bending,  and  is  further  obtained  by  neglecting  the  denomi- 
nator of  Formula  52. 

Considering  a  long  rod  A  B,  Fig.  88,  Case  I.,  pin-jointed  at 
each  end,  but  guided  at  A  so  that  A  remains  vertically  over  B, 


Case    I 

Bo#>  ends  fxn- jointed 


C*s>-    777" 


,££•££ 

13 


FIG.  88.-  -Variation  of  Strut  Formula,  with  Method 
of  Fixing  Ends. 


with   a    force  P   applied   at  each   end  of  the  rod,  then  if  the 
deflection  at  a  distance  *  x '  from  A  is  ' '  yl 


or 


Let 


=  M 


y  =  - 


-  E  I  .  ffiy 


dx* 


E  I . 


P 
El 


then  on  substitution  we  have 


This  is  a  differential  equation  satisfying  the  given  conditions, 
and  therefore  a  solution  of  this  equation  will  also  be  a  solution 


STRESSES  AND  STRAINS  IN  COMPONENTS        125 

of  the  problem.  Looking  at  this  differential  equation,  we  note 
that  l  y  '  is  a  function  such  that  its  second  derivative  must  be 
proportional  to  itself.  This  condition  is  satisfied  by  a  sine  or 
cosine  function  of  the  form 

y  —  a  sin  (b  x  +  c)  ............        2 

where  #,  £,  and  c  are  constants  to  be  determined  by  the  con- 
ditions of  the  case.  Since  this  is  a  function  of  the  sine,  we  see 
that  the  shape  into  which  the  column  will  be  bent  must  be 
sinusoidal. 

Differentiating  equation  2,  we  have 

dyjdx  =  abcos(bx  +  <r)  ...........       3 

Differentiating  equation  3,  we  have 

d'2yldx^  =  -aPsm(bx  +  c)      ............       4 

Substituting   in    equation    I    above  the   values  obtained    in 
equations  2  and  4,  we  have 

-  a  &  sin  (b  x  +  c)  =   -  /2  a  sin  (b  x  +  c) 

Cancelling  out  common  factors  and  taking  the  square  root 
we  obtain 


In  order  to  eliminate  the  constant  c)  we  must  consider  the 
end  conditions. 

When  x  =  o,  we  have  y  =  o,  and  on   substitution  in  equation  3 
we  obtain  a  sin  ^  =  o 

whence  c  =  o 

Again,  when  x  =  L,  then  y  =  O,  which  gives  b  L  =  IT      ......       6 

Substituting  the  value  thus  obtained  for  b  in  equation  5,  we  have 


L        V   EI 

7T2EI 

or     P  =        2  Formula  58 

It  should  be  noted  that  the  value  of  the  constant  'a'  has 
not  been  determined.  '  a '  represents  the  amplitude  of  the  sine 
curve,  and  since  the  fundamental  equation  is  satisfied  by  any 
amplitude  whatever,  we  have  no  restrictions  upon  the  value  of 
'  al  which  is  therefore  indeterminate. 

If  Formula  52  is  used  instead  of  Formula  53  for  the  deriva- 
tion of  this  theory,  the  solution  gives  rise  to  an  elliptic  integral. 


126  AEROPLANE    DESIGN 

The  theory  that  we  have  just  outlined  for  long  columns  is 
known  as  Euler's  Theory,  and  there  are  four  standard  cases  to 
be  considered. 

CASE  I. — The  case  we  have  just  considered,  namely  both  ends 
pin-jointed.  This  is  the  commonest  case  in  practice. 

CASE  II. — One  end  fixed,  the  other  end  free  to  take  up  any 
angular  position  or  to  move  laterally.  In  this  case  we  have 

P  =  — ry  Formula  59 

The  equivalent  pin-jointed  length  of  the  strut  is   =  2  L 

CASE  III. — Both  ends  fixed  in  position  and  direction.  In 
this  case  we  have 

2   Tf    T 

P  =  — j2 —          Formula  60 

The  equivalent  pin-jointed  length  of  the  strut  is   =  J  L 

CASE  IV. — One  end  fixed,  the  other  end  pin-jointed,  but 
restrained  from  lateral  movement. 

P  =  — r-r—         ,    .  Formula  61 

4L2 

The  equivalent  pin-jointed  length  of  the  strut  is   =  - 

In  using  Euler's  formula  the  greatest  working  load  is  found 
by  dividing  by  a  factor  of  safety,  and  the  load  so  obtained  must 
not  exceed  the  safe  crushing  load  for  the  given  material. 
Further,  the  given  load  must  be  applied  axially,  as  Euler's 
formula  does  not  apply  if  there  is  any  eccentricity.  Moreover 
the  formula  does  not  apply  to  struts  which  are  not  long  in  com- 
parison with  their  cross-sectional  dimensions.  For  aeronautical 
work  the  ratio 

length  of  the  strut 

least  radius  of  gyration 

should  be  greater  than  90  if  Euler's  formula  is  to  be  used. 

For  struts  which  are  not  long  compared  with  their  cross- 
sectional  dimensions  various  empirical  formulae  have  been 
devised,  the  best  known  and  most  widely  used  of  which  is  the 
Rankine-Gordon  formula.  This  is  of  the  form 

p  / 

p  =  —  =  T      2      Formula  62 

A  I    Li 

i.  *   +  a  \  ~I 

where  L  k 

p  is  the  crushing  or  crippling  load  on  strut  in  tons  (or  Ibs.)  per 
square  inch  of  cross-section. 


STRESSES  AND  STRAINS  IN  COMPONENTS        127 

P  is  the  crushing  or  crippling  load  in  tons  (or  Ibs.). 

A  is  the  cross-sectional  area  in  square  inches. 

f  is  the  direct  crushing  strength  of  the  material  of  the  strut  in  tons 

(or  Ibs.)  per  square  inch. 
a  is  a  constant. 

L  is  the  length  of  the  strut — pin-jointed — in  inches. 
k  is  the  least  radius  of  gyration  of  the  strut  in  inches. 


10000 


8000 


600O 


2000 


of     C'onsfanf'    in   the    Rank  in  e     o  Art/A  Form 


\ 


Ash' 


50 


100  rso 

of    Sfruf 


200 


250 


300 


of 


FIG.  89. 


By  experiment,  the  values  of  f  and  a  have  been  determined. 
For  aeronautical  work  Euler's  formula  is  generally  used  for  the 
Interplane  Struts  and  the  Spars,  and  for  spruce  the  value  of  E  is 
taken  as  1-6  x  io6 

For  the  fuselage  and  similar  short  struts  Rankine's  formula 
is  used,  and  for  spruce  f  is  taken  as  5000  Ibs.  per  square  inch, 
and  the  value  of  the  constant  (a'  as  1/5200,  when  Rankine's 
formula  becomes  for  spruce 

P  =  5ooo  *_&__o          Formula  62  (a) 


128 


AEROPLANE   DESIGN 


Strictly  speaking,  the  value  of  the  constant  ifa  should  vary 
with  the  value  of  L/£,  and  Fig.  89  gives  the  variation  of  this 
constant  for  value  of  L//£  up  to  300,  according  to  data  published 
by  the  R.A.F. 

For  ash, /"is  taken  as  6200  Ibs.  per  square  inch. 

Eccentric  Loading. — We  get  an  illustration  of  a  combined 
direct  and  bending  stress  when  a  strut  or  column  is  loaded 
eccentrically.  Let  Fig.  90  represent  such  a  case,  where  a 
load  F  is  applied  at  a  distance  x  from  the  centroid  line  of  the 
column.  Consider  any  section  such  as  XY.  Without  in  any 
way  affecting  the  stress  at  the  cross-section  X  Y,  we  could  insert 
equal  and  opposite  forces  F'  Y",  each  equal  to  F,  at  points  along 


J n 


I 

C|F' 

o  r' 


IQ 

FIG.  90. — Strut  loaded  eccentrically. 

P  Q,  such  as  c  and  D.  Due  to  F'  there  will  be  a  compressive 
stress  on  the  cross-section  X  Y  =  F'/A  =  F/A,  while  due  to  the 
couple  formed  by  F  and  F",  there  will  be  a  bending  moment  on 
the  cross-section  XY  =  F^r.  This  bending  moment  will  give  rise 
to  a  compressive  stress, 

F#  _  F  x  y       F  x  y 

~~ 


where  k  is  the  radius  of  gyration  of  the  section  in  the  plane 
of  bending.     Hence  the  total  compressive  stress  at  X  Y 

_  ,   _  F    ,    F  x  y 


A/*2 


=  -.-     i 


+  ^_ 


Formula  63 


STRESSES  AND  STRAINS  IN  COMPONENTS         129 


In  aeronautical  work  the  following  formula,  due  to  Professor 
Perry,  is  frequently  used  for  struts  with  eccentric  loading : 

Mf_Q 
Z 


/ 


Formula  63  (a) 


Where 


TJ- 

P  =  end  load 

M  =  maximum  bending  moment 
f  =  maximum  stress 
A  =  cross  sectional  area 
Z  =  modulus  of  section 


FIG.  91. — Dimensions  of  Stream-lined  Strut, 
Fineness  Ratio  3:1. 

Streamlined  Struts. — Fig.  91  gives  the  form  and  dimen- 
sions of  a  standard  stream-lined  strut. 

The  radius  at  A  is  *o8/,  from  A  to  B  is  75  /,  from  B  to  C  it  is 
2*25  tt  from  C  to  D  it  is  5*3  /,  and  at  D  it  is  *i  t.  The  total  length 
of  the  strut  is  3  /. 

The  cross-sectional  area  =  2'iQ/2 

The  Moment  of  Inertia  =  0*132  /4 

Ditto  (transverse)  =  riy/4 

Distance  of  C.G.  behind  leading  edge  =  i  '34  / 

Tapered  Streamline  Struts. — The  development  of  large 
machines  has  led  to  the  need  for  still  greater  economy  in  material 
and  weight.  In  such  machines  considerable  weight  can  be  saved 
by  the  use  of  tapered  interplane  struts.  The  theory  of  the 
correct  taper  for  such  struts,  and  its  application  to  actual  design, 
will  be  fully  treated  in  Chapter  V. 


CHAPTER  V. 
DESIGN  OF  THE  WINGS. 

Wing  Structures. — The  first  man  to  develop  a  form  of 
wing  construction  which  contained  all  the  essential  elements 
of  a  modern  aeroplane  wing  was  Henson,  who  as  early  as  1842 
adopted  the  Fink  Truss  for  his  wing  construction.  It  is  some- 
what surprising,  therefore,  that  the  earlier  experimenters  did  not 
adopt  Henson's  construction,  which  enabled  a  large  reduction  to 
be  made  in  the  number  of  exposed  wires  as  compared  with  the 
umbrella  type  of  wing  which  was  used  by  Lilienthal  and  other 
pioneers.  The  first  comparatively  modern  machine  to  be  fitted 
with  this  type  of  wing  structure  was  the  Antoinette  in  1909. 
This  was  somewhat  similar  in  form  to  the  type  shown  in 
Fig.  93A. 

Monoplane  Trusses. — Fig.  92A  shows  the  most  generally 
adopted  form  of  monoplane  bracing.  The  great  objections  to 
this  type  are — 

(a)  The  large  total  resistance  of  the  wires. 

(^)  The  heavy  compression  set  up  in  the  spars. 

The  stress  diagram  of  such  a  structure  illustrates  the  latter 
objection  very  clearly,  as  shown  by  Fig.  926.  It  will  be  noticed 
that  the  compression  in  the  spars  due  to  the  angularity  of  the 
lift  wires  becomes  very  marked  towards  the  centre  of  the  span. 
Moreover,  it  is  often  difficult  to  place  a  direct  strut  across  the 
fuselage,  where  the  wing  abuts.  The  advantages  of  this  type 
are  simplicity  of  construction  and  ease  of  adjustment. 

The  king-post  method,  shown  in  Fig.  93A,  has  the  advantage 
of  reducing  the  compression  in  the  spars  very  considerably. 
The  two  cabane  wires  can  be  arranged  at  a  good  angle,  and 
similarly  the  king-post  wires  can  be  at  a  greater  angle  than  a 
wire  from  the  cabane  to  the  outer  point.  The  compressions  in 
the  spars  between  the  king-post  bracing  wires  are  self-contained, 
that  is,  they  are  not  transmitted  to  the  portion  b  c,  which  suffers 
so  severely  by  the  accumulation  of  compression  in  the  most 
general  arrangement  shown  in  Fig.  92A.  The  maximum  com- 
pression occurs  in  the  portion  a  b.  This  arrangement  is 
particularly  useful  when  it  is  difficult  to  get  in  a  sufficiently 
strong  cross-fuselage  strut  such  as  would  be  required  in  the 
method  of  Fig.  92A. 


DESIGN    OF   THE  WINGS  131 

In  1910  Bleriot  adopted  the  Pratt  Truss,  already  popular  in 
biplane  construction,  for  his  monoplane,  which  was  of  consider- 
able span  and  of  the  type  shown  in  Fig.  94.  A  slightly  different 
construction  has  survived  until  the  present  time  in  the  German 
Taube.  In  the  early  days  of  aeroplane  construction  the  mono- 
plane achieved  prominence  in  comparison  with  the  biplane. 


F7g.  33 


Monoplane  Trusses. 


The  interference  factor  was  absent,  and  the  conception  of  the 
fuselage  brought  about  a  considerable  decrease  in  the  amount 
of  head  resistance.  A  greater  margin  of  power  became  avail- 
able, and  the  resulting  increase  of  velocity  enabled  a  reduction 
of  area  to  be  made ;  and  to  still  further  enhance  the  effect  better 
wing  sections  were  introduced.  The  popularity  of  the  mono- 


132  AEROPLANE    DESIGN 

plane  was  short-lived,  however,  first  on  account  of  its  inherent 
inferiority  as  a  structure,  and  secondly  owing  to  the  disappear- 
ance of  the  aerodynamical  disabilities  of  the  biplane  as  finer 
flying  angles  were  attained. 

Biplane  Trusses. — The  first  man  to  produce  a  simple  and 
statically  clear  structure  for  the  Biplane  Truss  was  a  bridge- 
builder,  Chanute,  one  of  the  early  pioneers  in  aeronautics.  He 
applied  the  Pratt  Truss  to  the  biplane,  and  the  idea  was 
immediately  adopted  as  the  standard  method  of  construction. 
Figs.  95-99  show  the  general  form  of  biplane  trusses,  the 
number  of  panels  varying  from  two  to  four  in  various  con- 
structions. By  varying  the  width  of  the  panels  as.  shown,  the 
structure  can  be  made  of  lighter  weight,  or  much  stronger  for 
the  same  weight.  The  forces  acting  in  the  spars  increase  from 
the  wing  tips  towards  the  body,  and  it  is  advisable  therefore  to 
reduce  the  length  of  the  spans  towards  the  centre  of  the 
machine.  This  arrangement  leads  to  a  greater  uniformity  of 
forces  in  the  members,  since  the  outer  struts  and  wires  will  be 
more  heavily  loaded  and  the  inner  members  less  heavily  loaded 
than  in  the  equally  divided  spans. 

The  next  advance  was  the  introduction  of  the  overhung  type 
of  biplane  truss  by  Henry  Farman.  This  type  is  shown  in 
Fig.  97.  The  overhang  is  treated  either  with  lift  wire  bracing 
or  with  a  landing  strut.  The  latter  arrangement  is  preferable, 
for  it  offers  less  resistance  to  motion.  This  is  an  important 
consideration,  particularly  for  high-speed  machines.  Attention 
has  already  been  drawn  to  the  fact  that  aerodynamically  the 
multiplane  is  less  efficient  than  the  monoplane,  owing  to  the 
interference  between  superimposed  planes,  the  lower  planes 
being  most  affected.  From  this  it  follows  that  the  greater  the 
percentage  of  the  total  area  formed  by  the  upper  plane,  the 
greater  will  be  the  efficiency  of  the  combination,  other  things 
being  equal.  Various  other  considerations,  however,  place  a 
limit  upon  the  reduction  of  the  lower  wing.  For  example,  if 
the  top  wing  be  retained  in  its  usual  biplane  position  above  the 
fuselage,  while  the  area  of  the  lower  wing  is  reduced  to  zero,  a 
monoplane  of  what  has  come  to  be  known  as  the  '  parasol '  type 
results.  In  such  a  machine  the  C.G.  is  very  much  below  the 
centre  of  lift,  and  the  centre  of  thrust  will  probably  be  some 
distance  below  the  centre  of  resistance.  This  is  undesirable 
for  several  reasons,  and  hence,  despite  the  unrestricted  view 
downwards  which  such  a  type  gives,  the  'parasol'  type  has 
never  developed.  This  case  illustrates  how  practical  require- 
ments tend  to  lessen  the  aerodynamical  efficiency  of  the  mono- 


DESIGN    OF   THE   WINGS 


133 


plane.  In  order  to  overcome  these  disadvantages  the  French 
firm  of  Nieuport  compromised  between  the  theoretical  efficiency 
of  the  monoplane  and  the  practical  advantages  of  the  biplane. 
They  effected  this  by  making  the  area  of  the  upper  planes  about 


** 


Biplane  Trusses. 


twice  that  of  the  lower,  thus  closely  approximating  to  the 
monoplane  aerofoil  efficiency  while  still  retaining  the  biplane 
construction.  The  resulting  machine  has  proved  very  successful. 
A  side  view  of  the  wing  structure  is  shown  in  Fig.  1 14. 

At  this  point  it  will  be  instructive  to  examine  the  stress 


134 


AEROPLANE    DESIGN 


diagram  for  a  general  type  of  biplane  of  about  the  same  size  as 
the  monoplane  shown  in  Fig.  Q2A.  The  stress  diagrams  for  the 
two  cases  are  shown  in  Fig.  100,  the  monoplane  at  A  and  the 
biplane  at  B.  The  biplane  has  been  arranged  so  that  the  aspect 
ratio  of  the  wings  is  the  same,  but  the  combined  area  of  the  two 
wings  is  about  20%  greater  than  that  of  the  monoplane  in  order 


FIG.  100. — Comparison  of  Stress  Diagrams  for  Monoplane  (A) 
and  Biplane  (B). 


to  allow  for  the  same  landing  speed,  the  maximum  lift  coefficient 
for  the  biplane  being  reduced  by  interference  at  large  angles. 
The  gap  is  equal  to  1*2  x  chord.  A  comparison  of  the  two 
stress  diagrams  shows  a  considerably  reduced  compression  in 
the  lower  spars  of  nearly  70%,  so  that  these  latter  could  be  made 
very  lightly.  The  biplane  thus  scores  rather  curiously  perhaps 


Wireless 


Rg.   101 


Biplane 


R&I02 


for  high-speed  work  where  the  wings  are  necessarily  thin  and 
the  maximum  thickness  of  the  spar  must  be  small.  Notice  that 
as  the  compression  due  to  angularity  of  the  lift  wires  of  a  mono- 
plane becomes  pronounced  as  the  span  is  increased,  so  also  the 
compressions  in  the  spars,  even  of  a  biplane,  mount  up  if  the 
span  is  unduly  increased. 


DESIGN  OF   THE   WINGS  135 

Wireless  Biplane  Trusses. — In  1913  the  Albatross  Com- 
pany of  Germany  introduced  what  have  come  to  be  known  as 
wireless  trusses.  An  example  is  shown  in  Fig.  101.  The 
advantage  resulting  from  this  construction  is  due  to  the  reduc- 
tion in  resistance  obtained  by  eliminating  both  lifting  and 
landing  wires  and  substituting  members  which  will  transmit 
both  compression  and  tension.  It  is  found  that  the  total  length 
of  all  the  web  members  of  a  wireless  truss  can  easily  be  made 
much  less  than  one- half  the  total  length  of  all  the  wires  and 


Fpg.  105 


Rg:  KM- 


Fig  105 


Triplane  Trusses. 


struts  of  the  usual  form  of  truss,  so  that  the  resistance  of  the 
web  members  can  be  reduced  almost  one-half  with  a  very  small 
increase  of  weight. 

Strutless  Biplane  Truss. — The  truss  shown  in  Fig.  102 
illustrates  a  very  unusual  departure  from  orthodox  practice  in 
biplane  construction.  This  type  of  truss  was  designed  by 
Dr.  Christmas  in  order  to  imitate  as  far  as  possible  the  flexi- 
bility of  the  wings  of  a  bird,  the  wing  tips  of  this  biplane  having 


i36 


AEROPLANE    DESIGN 


a  range  of  movement  of  eighteen  inches  from  a  mean  horizontal 
position  in  either  direction.  Thus  the  wings  can  assume  a 
negative,  neutral,  or  positive  dihedral  according  to  circumstances. 

Triplane  Trusses. — These  may  be  treated  in  exactly  the 
same  manner  as  those  of  the  biplane.  Figs.  103-105  show 
various  forms  of  bracing  a  triplane.  It  should  be  noted,  how- 
ever, that  in  the  method  of  Fig.  103  the  full  height  of  the  truss 
is  not  utilised,  and  as  a  result  the  strength  of  this  construction 
is  only  about  a  quarter  of  that  shown  in  Fig.  104.  The  triplane 
has  the  advantage  of  diminishing  the  length  of  the  struts  by  half, 
which  makes  them  relatively  much  stronger. 


WIRELESS  TRI PLANE  TRUSS. 


Fig.  IO6 


Q.UADRUPLANE1  TRUSS 


Fig.  107 


Wireless  Triplane  Trusses.— Fig.  106  shows  the  latest 
Fokker  triplane,  which  is  of  this  type.  As  will  be  seen,  all  lift 
and  landing  wires  are  abolished,  and  the  only  wires  used  are  the 
diagonal  cross  bracing  wires  between  the  centre  struts  sloping 
outwards  and  upwards  from  the  body  to  the  top  wing.  The 
designer  of  the  Fokker  seems  to  have  sacrificed  structural 
strength  in  order  to  cut  down  head  resistance  and  interference 
to  an  absolute  minimum.  Such  a  wing  structure  as  illustrated 
demands  a  very  deep  spar,  in  order  to  obtain  a  large  moment  of 
inertia  coupled  with  a  small  area  of  section.  In  the  spar  con- 


DESIGN   OF   THE   WINGS  137 

struction  adopted  by  the  Fokker  we  find  the  two  spars  of 
an  ordinary  wing  structure  are  placed  rather  closer  together 
than  usual.  These  spars  are  approximately  of  the  ordinary  box 
shape,  and  are  made  into  one  compound  section  by  means  of 
three-ply,  and  internal  wing  bracing  is  omitted.  (See  Fig.  141.) 

Quadruplane  Trusses. — The  quadruplane  truss  shown  in 
Fig.  107  illustrates  an  attempt  made  by  Messrs.  Armstrong, 
Whitworth,  &  Co.  to  supply  a  machine  possessing  good  visi- 
bility in  all  directions,  and  therefore  of  great  service  as  a 
fighting  scout.  The  performance,  however,  is  not  so  good  as  a 
comparatively  small  biplane,  and  pilots  report  that  the  machine 
is  not  an  easy  one  to  fly. 

Drag  and  Incidence  Bracing. — So  far  we  have  considered 
only  the  lift  truss  of  an  aeroplane.  In  order  to  stiffen  the  wings 
in  the  horizontal  plane  drag  bracing  is  used.  This  in  general 
takes  the  form  shown  in  Fig.  108  for  all  types.  The  spars  are 
braced  together  by  means  of  the  tie  rods  *  K  '  and  compression 
members  '  C.'  For  small  machines  specially  constructed  ribs, 
termed  compression  ribs,  are  sufficient  to  withstand  the  com- 
pressive  forces  between  the  two  spars ;  but  for  large  machines, 
and  also  in  cases  where  the. lift  bracing  is  duplicated  through 
the  incidence  wires,  steel  tubes  or  wooden-box  struts  are  neces- 
sary to  take  the  compression.  The  spars  themselves  transmit 
the  components  of  the  stress  in  the  wires  in  the  direction  shown 
by  the  arrow,  and  these  stresses  must  be  added  to  those  in  the 
spars  due  to  the  lift  forces.  The  lift  and  drag  trusses  are 
combined  to  form  a  rigid  three-dimension  structure  by  means  of 
bracing  in  planes  passing  through  the  struts  and  parallel  to  the 
plane  of  symmetry  of  the  whole  machine.  This  side  bracing  is 
usually  termed  INCIDENCE  BRACING.  In  the  case  of  the  mono- 
plane, the  most  usual  form  is  shown  in  Fig.  109.  Each  wing 
has  two  parallel  or  slightly  converging  spars — front  and  rear. 
The  front  pair  of  spars,  together  with  some  central  pylon  or  the 
landing  chassis  taken  as  a  kingpost,  forms  the  front  lift  truss, 
the  rear  lift  truss  being  formed  in  a  similar  manner. 

For  the  biplane  the  most  common  types  of  incidence  bracing 
are  shown  in  Figs.  1 10  and  1 1 1,  adapted  to  straight  and  staggered 
biplanes  respectively.  The  incidence  bracing  may  also  be  used 
to  transmit  the  shear  due  to  the  lift  or  down  forces  from  one 
frame  to  the  other,  if  either  of  the  bracing  wires  of  the  lift  truss 
are  broken.  For  example,  suppose  one  of  the  front  lift  wires  of 
a  machine  were  shot  away,  the  force  which  was  originally  trans- 
mitted to  the  body  by  this  v/ire  can  be  transferred  by  the 


AEROPLANE   DESIGN 

incidence  bracing  to  the  rear  frame  and  carried  along  to  the 
body  through  this  system.  By  this  method  it  is  possible  to 
avoid  the  direct  duplication  of  the  main  bracing  wires,  thereby 
considerably  reducing  the  head  resistance  of  the  machine.  It 
should,  however,  be  observed  that  the  stress  in  the  incidence 


Rg:  ioa       DRAG   BRACING 


c 


I  NCIDLNCE      BRACINQ 


FIG.  in 


RQ.  "3 


FIG.  H4- 


F.Q.  US 

Types  of  Drag  and  Incidence  Bracing. 

bracing  will  give  rise  to  an  increased  force  in  the  drag  bracing, 
which  must  be  made  correspondingly  stronger  if  this  method  is 
adopted.  Figs.  112  and  113  show  the  *N'  type  side  bracing, 
with  which  again  the  resistance  of  the  ordinary  bracing  can  be 
decreased  by  half.  This  bracing,  especially  when  combined 
with  the  wireless  lift  truss  (Fig.  101),  offers  considerable  possi- 


DESIGN   OF   THE   WINGS  139 

bilities  for  heavy  large-span  aeroplanes.  Fig.  114  shows  the 
'v'  type  side  bracing  used  in  the  Nieuport  scouts.  The  two 
converging  struts  are  fixed  in  a  special  socket  fitted  upon  the 
spar  of  the  lower  plane.  This  construction  is  adaptable  to  both 
straight  and  staggered  biplanes,  but  in  both  cases  is  especially 
good  for  an  unequal  chord  biplane. 

Development  of  the  Single  Lift  Truss. — In  1909  Breguet 
produced  a  single  lift  truss  biplane,  and  in  1914  the  R.A.F. 
adopted  this  construction  for  a  fast  scouting  machine.  A  side 
view  of  such  a  machine  would  be  somewhat  as  shown  in 
Fig.  115.  The  struts  were  fixed  in  sockets  having  long  bases 
that  reached  from  the  front  spar  to  the  rear  spar,  and  were  fixed 
to  the  latter.  The  front  and  rear  parts  of  the  socket  base  may 
then  be  considered  as  a  cantilever,  subject  to  bending  as  the 
centre  of  pressure  of  the  aerofoil  moves  in  front  of  or  passes 
behind  the  centre  of  the  strut.  The  struts  are  thus  subject 
not  only  to  compression,  but  also  to  bending.  The  bending 
moments,  however,  are  comparatively  small  for  the  ordinary 
size  of  machine,  and  can  easily  be  accounted  for. 

The  advantages  of  the  single  lift  truss  are  : — 

1.  A  reduction  in  weight  and  resistance  of  the  struts. 

2.  A  reduction  in  resistance  of  the  bracing  wires. 

3.  The   forces    acting   are    practically   independent   of   the 

position  of  the  C.P.,  whereas  in  the  double  lift  truss  in 
the  extreme  attitudes  of  flight  one  of  the  trusses  is 
partly  idle,  and  consequently  contains  excess  strength 
and  weight. 
Generally  the  forces  acting  on  a  single  lift  truss  will  be  about 

30%  less   than  the  maximum  load,  thus  leading   to  a  further 

reduction  of  weight  and  air  resistance. 

Tractor  and  Pusher  Machines. — All  aeroplanes  at  present 
constructed  may  be  classified  under  one  of  the  above  types,  or 
as  a  combination  of  both  types.  As  a  generalisation  it  may  be 
said  that  the  fundamental  difference  between  the  two  types  is 
that  in  the  tractor  machine  the  airscrew  is  placed  in  front  of 
the  wing  structure,  whereas  in  the  pusher  machine  it  is  placed 
behind.  Side  views  of  the  two  types  are  shown  in  Figs.  1 16  and 
117  (page  144),  from  which  it  will  be  seen  that  the  change  in  the 
position  of  the  engine  and  airscrew  considerably  modifies  the 
form  of  the  body.  In  the  case  of  the  tractor,  the  body  (or 
fuselage)  extends  from  the  airscrew  at  the  extreme  front  right 
down  to  the  control  surfaces  at  the  extreme  rear  of  the  machine. 
Such  a  body  can  with  care  be  made  of  excellent  streamline 


140  AEROPLANE    DESIGN 

form,  and  if  totally  enclosed — which  is  likely  to  become  standard 
practice  in  the  near  future — a  comparatively  low  resistance  can 
be  obtained.  In  the  case  of  the  pusher,  the  presence  of  the 
airscrew  at  the  rear  of  the  wing  structure  necessitates  a  different 
form  of  construction  in  order  to  connect  the  control  surfaces  to 
the  wing  structure.  This  takes  the  form  of  what  is  known  as 
an  'outrigger,'  consisting  usually  of  four  longitudinal  booms 
stretching  from  the  wings  at  points  where  they  are  of  sufficient 
distance  apart  to  allow  the  airscrew  to  rotate  between  them, 
/  out  to  the  tail  unit.  The  body  of  a  machine  of  this  type  is  termed 
a  nacelle,  and  is  situated,  as  shown  in  Fig.  116,  in  front  of  the 
wings,  thereby  enabling  an  excellent  range  of  vision  and  of 
gunfire  to  be  obtained.  It  is  comparatively  short,  however, 
and  the  position  of  the  engine  prevents  a  good  streamline  shape 
from  being  obtained. 

In  making  a  comparison  of  the  aerodynamical  efficiency  of 
the  two  types,  it  must  .be  noted  that  the  fuselage  of  the  tractor 
machine  is  operating  in  the  slip  stream  of  the  airscrew,  which 
leads  to  an  increase  in  its  resistance.  In  practice  it  is  found 
that  the  presence  of  the  fuselage  in  the  wake  of  an  airscrew 
increases  the  efficiency  of  the  airscrew,  and  these  two  factors 
must  therefore  be  considered  in  conjunction  with  one  another. 
In  the  pusher  type  of  machine,  the  less  efficient  type  of  the 
nacelle  is  coupled  with  a  loss  in  efficiency  of  the  airscrew  due 
to  the  obstructed  flow  of  the  airstream  in  front  of  its  path.  It  is 
therefore  apparent  that  the  tractor  type  is  much  more  efficient 
aerodynamically.  It  is  due  to  this  fact,  together  with  the  more 
rigid  structure  that  can  be  obtained  by  using  a  fuselage,  that  the 
pusher  type  of  machine  is  rapidly  disappearing. 

The  Factor  of  Safety. —The  question  of  the  factor  of 
safety  is  of  vital  importance  in  aeroplane  design.  Contrary  to 
general  engineering  practice,  the  structural  parts  of  an  aeroplane 
are  designed  to  have  a  certain  '  factor  of  safety '  with  reference 
to  the  normal  flying  load  determined  by  the  weight  of  the 
machine.  Any  excess  stress  due  to  manoeuvring  is  taken 
account  of  in  the  factor  of  safety  itself,  so  that  in  the  engineering 
sense  it  is  not  a  factor  of  safety  at  all,  but  merely  an  allow- 
ance for  additional  stresses  set  up  under  conditions  other  than 
ordinary  horizontal  flight.  It  is  possible  to  determine  approxi- 
mately what  the  maximum  stresses  are  likely  to  be,  and  from 
these  determinations  the  aeroplane  is  designed  so  that  its 
strength  at  all  points  is  sufficient  to  withstand  a  reasonable 
value  of  this  maximum  stress,  the  actual  4  factor  of  safety ' 
being  generally  below  2.  See  Table  X.,  page  24. 


DESIGN   OF   THE   WINGS  141 

In  no  other  branch  of  engineering  is  it  so  essential  on  the 
score  of  weight  to  use  so  small  a  margin  of  excess  material,  nor 
is  there  such  a  likelihood  of  greatly  increased  loads  being  placed 
suddenly  upon  the  structure  ;  while,  generally  speaking,  failure 
in  even  apparently  insignificant  details  leads  to  disastrous  re- 
sults. The  requisite  factor  to  adopt  in  any  particular  case  follows 
more  or  less  upon  the  selection  of  type ;  it  is  obvious,  for 
instance,  that  a  fairly  heavy  biplane  will  not  be  '  stunted  '  in 
the  air  to  the  same  extent  that  a  scout  would  be,  while  a  heavy 
commercial  or  passenger-carrying  machine  will  be  most  care- 
fully handled  in  the  air.  Bearing  these  facts  in  mind  we  may 
examine  the  more  important  conditions  common  to  all  types  in 
flight  which  tend  to  increase  the  normal  load. 

The  load  supported  by  the  wings  equals  the  weight  of  the 
complete  machine  only  when  the  vertical  component  of  flight  is 
without  vertical  acceleration  and  the  direction  of  the  wind  is 
steady.  This  second  condition  is  necessary  because  a  sudden 
change  of  the  vertical  component  by  the  action  of  the  wind 
might  produce  an  overload  by  its  impulsive  action  without 
causing  any  appreciable  difference  in  the  motion  of  the  aero- 
plane. The  maximum  loading  which  can  occur  in  this  and 
similar  cases  is  assessed  by  imagining  the  aeroplane  to  be  flying 
at  its  fastest  horizontal  speed  and  to  be  suddenly  pitched  from 
the  angle  of  incidence  corresponding  to  that  speed,  to  the  angle 
of  maximum  lift.  The  loading  would  then  be  momentarily 
increased  in  the  ratio  approximately  of  the  lift  coefficients.  As 
the  maximum  lift  coefficient  for  any  normal  wing  does  not  vary 
greatly  from  0*6,  the  factor  of  safety  necessary  here  will  depend 
practically  on  the  fastest  flying  speed.  This  is  one  reason  why 
the  fast  machine  should  have  a  higher  factor  of  safety  than  the 
slow  machine.  It  is  evident  that  such  change  of  motion  may 
take  place  from  accidental  causes  and  may  be  in  the  negative 
as  well  as  in  the  positive  direction,  thus  throwing  a  load  on 
the  '  down '  bracing  of  a  biplane,  or  on  the  upper  wires  of  a 
monoplane. 

Vertical  motion  due  to  the  air  may  be  classed  under  two 
heads : — 

1.  Alteration  of  wind  velocity.     In  this  case   the  effect  is 
similar  to  pitching  if  the  vertical  component  only  of  the  wind 
velocity  changes,  but  is  more  serious  if  combined  with  a  change 
due  to  gusts. 

2.  The  action  of  air  pockets.     Air  pockets,  which  are  really 
currents  of  air  of  different  velocities  from  that  of  the  main  air- 
stream,   often    occur   over   rivers,   etc.      The   effect   so   far    as 
concerns  us  here  is  that  of  dropping  the  aeroplane  a  certain 


142  AEROPLANE   DESIGN 

distance,  and  then  dealing  with  the  resistance  of  the  wings  as  at 
90°  incidence,  and  having  the  velocity  acquired  by  the  fall. 
The  distance  fallen  will  not  be  large  and  as  the  aeroplane 
is  continuously  air-borne  to  some  extent,  this  effect  should  not 
result  in  any  considerable  overloading 

An  illustrative  example  will  make  this  clear. 

A  biplane  of  300  sq.  ft.  wing  area  enters  an  air  pocket  and 
falls  through  a  height  of  25  ft.  Find  the  increase  of  force  on 
the  wings  when  the  machine  emerges  into  air  of  normal  density. 
Take  the  resistance  of  the  wings  as  equal  to  '003  A  V'2 

The  vertical  velocity  downwards  is  given  by  the  relationship 


=    2    X    32-2    X    25 

.'.  V  =  40  f.p.s. 
R  =  -003  A  V2 

=  '003  x  300  x  40  x  40 

=  1440  Ibs. 

=  increase  of  force  on  wings. 

Another  condition  in  which  loading  may  be  augmented  is  in 
turning.  During  this  manoeuvre  the  machine  is  banked  to 
prevent  side-slipping  outwards,  hence  the  overloading  depends 
entirely  upon  the  sharpness  of  the  turn,  that  is,  upon  its  radius  ; 
and  the  amount  of  banking. 

Let  W  =  the  weight  of  the  machine. 
V  =  the  velocity  of  the  machine. 
R  =  the  radius  of  the  turn. 
ft  =  the  angle  of  banking  proper  to  the  turn.     (See  Fig.  118.) 

Then,  if  circular  turning  is  assumed,  the  force  acting  inwards 
towards  the  centre  of  turning  =  W  V2/£-  R. 

This  force  must  be  applied  as  a  lift  practically  normal  to  the 
plane  of  the  wings,  and  hence  the  force  on  the  wings  due  to 
banking  =  (  W  V2  fg  R)  sin  /3. 

When  the  wings  are  banked,  however,  the  weight  of  the 
machine  is  taken  by  only  a  component  of  the  forces  on  the 
wings.  The  load  due  to  the  weight  =  W  /  cos  /3,  so  that  the 
loading  is  increased  from  two  causes.  In  a  very  sharp  turn  the 
the  bank  may  be  very  steep  and  the  machine  may  be  allowed 
to  fall  during  the  very  short  time  necessary  for  the  turn. 

The  minimum  possible  radius  of  turning  occurs  when  the 
centrifugal  force  exerted  towards  the  centre  of  turning  is  the 
maximum  aerodynamically  possible.  This  obtains  when  the 
wing  is  banked  approximately  vertically  and  is  inclined  to  the 


DESIGN    OF   THE   WINGS  143 

flight  path  at  the  angle  of  maximum  lift.  The  question  of  over- 
loading which  occurs  at  about  the  commencement  of  the  turn  is 
then  similar  to  the  case  of  pitching  already  considered. 

An  illustrative  example  will  help  to  make  this  condition 
clear. 

A  machine  weighing  1800  Ibs.  is  travelling  at  100  m.p.h.  and 
is  suddenly  banked  to  an  angle  of  60°.  To  find  the  approxi- 
mate radius  of  turn  required  if  the  loading  on  the  wings  during 
the  turn  is  not  to  exceed  three  times  the  weight  of  the  machine. 

V  =  146-7  f.p.s. 
Force  acting  inwards 

WV2    . 


W  x  146*7  x  146*7  x  sin  60° 
32-2  x  R 

=  3  x  W     from  the  stated  conditions 
whence        R  =  193  feet. 


From  what  has  been  said  it  will  be  clear  that  the  speed  of  a 
machine  is  an  essential  factor  in  the  consideration  of  the  over- 
loading of  wings,  and  hence  it  is  natural  to  expect  the  over- 
loading to  be  a  maximum  when  the  speed  is  greatest.  This 
maximum  speed  will  probably  occur  in  a  long  nose  dive.  The 
following  example  is  instructive.  Suppose  a  machine  weighing 
1 200  Ibs.  and  fitted  with  a  100  h.p.  motor  is  capable  of  attain- 
ing 100  m.p.h.  in  horizontal  flight.  Take  the  ratio  of  L/D  of  the 
wings  at  this  speed  as  10  and  the  airscrew  efficiency  as  80%. 
To  find  the  terminal  velocity  at  the  end  of  a  long  nose  dive. 
The  lift  of  the  wings  must  equal  the  weight  of  the  machine, 
hence  since  the  L/D  ratio  is  10,  the  resistance  of  the  wings  at 
this  angle  will  be  =  1200/10  =  120  Ibs.  The  thrust  of  the 
airscrew  equals 

100  x  -8  x  550  x  3600 

— - —        -  =  300  IDS. 
100  x  5280 


144  AEROPLANE   DESIGN 

Hence  the  resistance  of  the   machine  less  the  wings  =  300  — 
1  20  =  1  80  Ibs. 

The  drift  coefficient  at  the  angle  of  no  lift  will  be  slightly 
greater  than  at  fastest  flying  angle.  A  reasonable  figure  would 
be  15  °  greater,  so  that  the  drift  of  the  wings  at  the  angle  of  no 


lift  =  120  x  1-15  =  138  Ibs. 

The  machine  will  have  acquired  its  maximum  possible 
velocity  downwards  when  the  weight  of  the  machine  is  equal  to 
the  resistance  of  the  air  ;  so  that  if  V  be  this  maximum  velocity, 
we  have  1200  =  [(138  +  180)  V  x  V]  /  100  x  100,  whence  V  = 
194  m.p.h.,  say  200  m.p.h. 

Since  the  speed  of  the  machine  is  thus  practically  doubled, 
the  drift  of  the  wings  will  be  increased  four  times  during  the 
last  portion  of  the  dive,  thus  causing  considerable  overload  of 
the  drift  wires. 

A  more  serious  overloading  will  occur  when  the  machine  is 
flattened  out  at  the  conclusion  of  the  nose  dive.  If  we  imagine 
it  to  have  been  flying  with  a  lift  coefficient  of  0*15  and  to  have 
a  maximum  lift  coefficient  of  O'6  ;  then  the  wings  will  be  over- 
loaded sixteen  times  for  a  sudden  impulsive  flattening  out. 
The  radius  of  the  flattening-out  curve  will  be 


. 
32  *2  x  16 

In  actual  flight  a  machine  does  not  answer  to  its  controls 
instantaneously,  so  that  the  impulsive  overloading  will  not  reach 
so  high  a  figure  as  that  indicated  ;  nevertheless  it  may  reach  an 
overload  as  great  as  twelve  times  the  weight  of  the  machine. 

In  order  that  the  overloading  should  not  exceed  four  times 
the  weight  of  the  machine,  the  radius  of  the  curve  must  there- 
fore be  4  x  170  ==  680  feet,  which  is  quite  a  large  radius  ;  while 
the  angle  of  the  wings  to  the  flight  path  must  not  exceed  the 
fastest  flying  angle,  the  maximum  lift  coefficient  being  O'i5- 

It  is  evident  from  this  example  that  it  is  practically  impos- 
sible to  design  an  aeroplane  which  shall  be  sufficiently  strong  to 
be  aerodynamically  'fool  proof  in  the  hands  of  the  pilot  if 
ample  control  is  provided.  It  is  necessary  therefore  to  com- 
promise on  the  matter  and  to  design  a  machine  with  a  factor  of 
safety  sufficient  to  meet  emergencies  but  with  certain  very 
definite  limitations  with  which  the  pilot  should  be  acquainted. 
This  is  particularly  the  case  with  machines  having  low  head 
resistance  and  which  as  a  consequence  may  develop  an  alarm- 
ingly high  speed  in  a  straight  nose  dive.  The  factor  of  safety 
hitherto  dealt  with  is  essentially  an  aerodynamic  one.  A  further 
margin  of  strength  is  required  to  deal  with  — 


Reprodttced  by  courtesy  of  Messrs,  dickers,  Ltd, 

FIG.  116 — '  Vickers  Vampire'  :  Armoured  Trench  Fighter, 
fitted  with  200  h.p.  B.R.2  Engine. 


Reprodticed  by  courtesy  of  Messrs.  Vickers>  Ltd.'l 

FIG.  117. — '  Vickers  16  D'  Scout,  fitted  with  200  h.p.  Hispano  Engine. 

Facing  page  144. 


DESIGN   OF   THE   WINGS  145 

1.  The  extra  stresses  produced  by  the  failure  of  one  of  the 
members  ; 

2.  The    extra    stresses    produced    in    the   building   of    the 
machine. 

The  first  requirement  is  of  great  importance  in  the  case 
of  military  machines  where  an  exposed  part  is  liable  to  be 
shot  away  or  seriously  weakened  by  a  bullet.  The  second  is 
liable  to  occur  owing  to  the  uneven  or  excessive  tightening  up 
of  the  bracing  system. 

The  general  overloading  produced  in  what  may  be  termed 
abnormal  flight  is  to  be  allowed  for  in  the  design  of  the  wings 
and  attachments  by  assuming  the  load  to  be  several  times  the 
flying  weight  of  the  machine,  the  multiplying  factor  varying  for 
different  aeroplanes  according  to  the  purpose  for  which  they  are 
designed.  Attention  must  be  given  to  the  stresses  induced  by 
the  breaking  of  a  part,  and  a  good  design  will  provide  against 
this  wherever  possible.  Stresses  due  to  counterbracing  must  be 
allowed  for,  but  in  building  the  machine  it  is  essential  to  take 
the  utmost  care  that  these  stresses  are  not  unduly  increased,  and 
that  in  '  tuning  up  '  (a  phrase  sometimes  used  to  describe  the 
forcible  straining  of  bad  work  into  its  correct  shape),  the 
mechanics  are  not  given  too  free  a  hand. 

Experimental  Investigation  of  the  Stresses  upon  a 
Full-size  Machine  during  Flight. — One  of  the  fundamental 
formulae  of  applied  mathematics,  which  follows  directly  as  a 
deduction  from  Newton's  Second  Law  of  Motion,  states  that 

Force  =  Mass  x  Acceleration. 

For  an  aeroplane  in  flight,  the  mass  is  practically  constant, 
hence  a  determination  of  the  forces  set  up  in  the  wing  structure 
will  follow  from  a  knowledge  of  the  acceleration  of  the  machine 
under  various  conditions.  This  principle  has  been  adopted  in 
the  full-scale  experiments  carried  out  at  the  Royal  Aircraft 
Establishment.  An  instrument  called  an  Accelerometer  is  used 
to  indicate  photographically  the  acceleration  of  the  machine  in 
terms  of  the  earth's  attraction — that  is,  in  terms  of  the  force  of 
gravity.  In  addition  to  giving  a  measure  of  the  resultant  air 
force  on  the  machine,  the  instrument  also  measures  the  time  of 
rapid  manoeuvres. 

Figs.  119  and  120  show  records  obtained  from  this  instru- 
ment in  actual  use.  Fig.  119  indicates  the  accelerations  set  up 
on  an  S.  E.  5  Scout  machine  and  a  Bristol  Fighter  during  a 
mock  fight,  while  Fig.  120  indicates  the  accelerations  and  speeds 
of  flight  of  a  Bristol  Fighter  during  various  manoeuvres.  It  will 

L 


146 


AEROPLANE    DESIGN 


be  observed  that  in  the  case  of  the  S.  E.  5  the  maximum  stresses 
nowhere  exceed  three  times  the  weight  of  the  machine.  In  the 
case  of  the  Bristol  Fighter  when  manoeuvring,  the  maximum 


I 


b/D 


•2 


! 

'•*•* 


-  o  «  •»»}  w-  O 


stress    occurs   during   a 


loop,  and  is  less  than    four  times  the 

weight  of  the  machine.     The  diagrams  indicate  that  the  stresses 
in  the  machines  keep  remarkably  steady  during  flight. 


DESIGN    OF   THE   WINGS 


147 


•0 


.b  -c 

<  PQ 


Accelerations  in  terms  of  g. 


148  AEROPLANE    DESIGN 

/  Stresses. — The  stresses  to  which  the  members  of  an  aero- 
plane are  subjected,  and  which  it  is  necessary  to  consider  in 
design,  are  as  follows  : — 

1.  Stresses  set  up  in  the  wing  structure  during  flight.    These 
may  be  sub-divided  into  two  classes : 

(a)  Those  due  to  Lift  and  Down  forces.  These  forces  are 
j>rincipally  transmitted  by  the  external  bracing  of  the 
machine. 

(fr)  Those  due  to  the  Drag  forces.  These  forces  are  trans- 
mitted by  the  internal  (or  the  drag)  bracing. 

2.  Stresses  set  up  in  the  wing  structure  and  under-carriage 
during  landing.     The  resultant  landing  shock  may  be  resolved 
into  a  vertical  component  known  as  '  down  shock/  and  a  hori- 
zontal component  known  as  '  end  shock.'     The  extent  of  these 
forces    is    dependent    upon   the    slope    at    which    the    machine 
descends,  and  the  nature  of  the  landing-ground. 

3.  Stresses  set  up  in  the  fuselage  due  to  the  operation  of  the 
control    surfaces,    and   to  the  thrust   of  the    airscrew.      When 
rotary    engines    are    fitted,    there    are   also   gyroscopic   effects 
developed. 

The  consideration  of  these  stresses  will  be  dealt  with  as 
follows :  The  stresses  resulting  from  the  various  conditions 
arising  in  flight  will  be  treated  in  this  chapter  ;  those  due  to 
landing  conditions  will  be  considered  in  the  chapter  on  the 
landing  chassis  ;  while  the  fuselage  stresses  will  be  investigated 
in  Chapter  VII. 

Stresses  in  the  Wing  Structure. — The  process  of  de- 
termining the  stresses  in  a  wing  structure  consists  of — 

1.  Finding  what  proportion    of  the    load   is  carried  by  the 
various  parts  of  the  structure. 

2.  Determining   what   stresses    these    loads    induce   in    the 
members  of  the  structure. 

In  dealing  with  the  first  part  of  the  problem  it  is  necessary 
to  know  (a)  the  distribution  of  loading  along  the  span  of  the 
wing  ;  (b}  the  distribution  of  the  load  over  a  section  of  the 
aerofoil. 

The  first  of  these  two  considerations  is  largely  dependent 
upon  what  is  termed  'end  effect.'  Unless  specially  determined 
data  for  the  wing  section  to  be  used  is  known,  it  is  customary 
to  assume  the  load  grading  near  the  wing  tips  as  being  para- 
bolic, the  variation  extending  for  a  distance  equal  to  the  chord 
from  the  wing  tips.  We  shall  return  to  this  point  again  later. 
The  second  consideration,  the  distribution  of  pressure  over  the 


DESIGN   OF   THE   WINGS 


149 


wing  section,  has  been  fully  considered  in  Chapter  III.  There 
remains  to  be  determined  what  proportion  of  the  load  is  carried 
by  the  spars  at  the  minimum  and  maximum  flying  angles.  This 
clearly  depends  upon  the  position  of  the  centre  of  pressure  of 
the  section  at  these  angles.  The  actual  travel  of  the  C.P.  for  the 
wing  section  adopted  must  be  found  by  reference  to  its  aero- 
dynamical characteristics.  In  general,  it  is  found  that  at  large 
angles  of  incidence,  corresponding  to  slow  speeds,  the  C.P.  is  at 
about  0-3  x  chord  from  leading  edge,  while  at  small  angles  and 
high  speed  it  is  at  about  0*5  X  chord.  As  an  example,  consider 
the  wing  section  shown  in  Figure  i?i. 

For  a  travel  of  the  C.P.  from  0*3  to  0-45  of  the  chord,  we 
have— Maximum  proportion  of  total  load  on  front  spar  = 
(44— i2*8)/44  =  71  ;  maximum  proportion  of  total  load  on 
rear  spar  =  (44  -  12)  {44  =  73. 


FIG.  121. 

Care  must  of  course  be  taken  when  determining  these 
stresses  that  the  most  unfavourable  condition  is  considered. 
Thus,  in  the  above  example,  the  front  spars  are  stressed  for  the 
most  forward  position  of  the  C.P.  ;  while  the  rear  spars  are 
stressed  for  the  most  backward  position  of  the  C.P.  In  this 
manner  the  maximum  possible  stresses  in  either  frame  are 
determined. 


Wing  Loading. — Wing  loading  may  be  defined  as  the  ratio 
weight  of  machine  :  area  of  supporting  surface.  Hence  from  the 
fundamental  equation  (Formula  i)  we  have 

—  -  loading  =  £  Ky  V 2 
A  g 

The  value  of  wing  loading  depends  upon  the  maximum 
speed  of  the  machine.  For  very  fast  machines  the  wing  loading 
is  high,  while  for  a  slow  machine  it  is  generally  low.  The 
advantage  of  a  low  value  of  wing  loading  is  that  it  gives  a  large 
margin  of  safety  against  excessive  loads.  Such  a  machine  will 


150  AEROPLANE   DESIGN 

require  more  engine-power  to  fly  at  a  given  speed  than  will  a 
machine  with  high  wing  loading.  The  general  tendency  to-day 
is  to  adopt  a  higher  wing  loading  than  was  formerly  used,  and 
the  majority  of  machines  in  present  use  have  a  wing  loading 
factor  of  from  7  to  10  Ibs.  per  square  foot. 

Table    XXV.,   giving   particulars   of  some    of    the   leading 
machines  of  the  day,  is  very  instructive  in  this  respect. 


TABLE  XXV. — WING  LOADING  OF  MODERN  MACHINES. 

Machine.  Wing  Area.  Weight.  Loa ding. 

Sq.  feet.  Lbs.  Lbs.  /  sq.  feet. 

Airco  4     434  •••        3340  ...  7-4 

Airco  9 438  ...       3351  ...  7-6 

Airco  10               ...          ...  840  ...       8500  ...  io-i2 

A.  R.  (French) 484  ...       2750  ...  5  72 

Avro         ...          ...          ...  346  .  .        2680  ...  8*23 

A.  W.  Quadruplane         ...  400  ...       1800  ...  4-5 

Blackburn  Kangaroo       ...  868  ...       8017  ...  9*2 

Breguet 528  ...       3380  ...  6-38 

Bristol  Fighter     ...         ...  405  ...       2630  ...  6-5 

Bristol  Monoplane           ...  145  ...       1300  ...  8*97 

Bristol  Triplane    ...          ...  1905  ...  16200  ...  8*50 

Bristol  All  Metal 458  ...       2810  ...  6*13 

Caproni 990  ...       8730  ...  884 

Caproni  Triplane             ...  2690  ...  14630  ...  5-45 

Caudron 427  ...       3170  ...  7-42 

Fokker  Triplane 215  ...        1260  ...  5-9 

F.  F.  Bomber  (German)...  750  ...       6950  ...  9-3 

Handley  Page  6-400     ...  1645  ...  14000  ...  85 

Handley  Page  V- 1 5 oo  ...  2950  ...  28000  ...  9*5 

Morane  Parasol  ...         ...  145  ...        1440  ...  9*92 

Nieuport  ...         ...         ...  160  ...        1200  ...  7^47 

S.  E.  5      ...         ...          ...  249  ...        1980  ...  8*0 

Sopwith 344  ...        2040  ...  5-93 

Sopwith  Camel    ...         ...  231  ...       1440  ...  6*2 

Sopwith  Dolphin...          ...  258  ...        1910  ...  7*4 

Sopwith  Snipe      ...         ...  274  ...       1950  •••  7'i 

Sopwith  Triplane             .  251  ...       1500  ...  6'o 

Spad         195  ...       1550  ...  8-08 

Vickers' Commercial       ...  1330  ...  11120  ...  8-4 


Wing  Weights. — The  wing  weight  varies  as  the  wing 
loading  per  square  foot  of  surface,  and  ranges  from  0*5  Ibs. 
per  square  foot  on  small  machines  up  to  1*4  Ibs.  per  square 
foot  on  very  large  machines.  The  following  formula  for  the 


DESIGN    OF   THE    WINGS  151 

weight    of    aeroplane   wings   are   taken    from    the    1911-1912 
N.P.L.   Report  : 

1.  Weight  of  Monoplane  wing  =  o  017  W(A)*  +  0*16  A 

2.  Weight  of  Biplane  wing       =  0-012  W(A)i  +  0-16  A 

where     W  =  weight  of  machine  less  the  weight  of  the  wings. 
A  =  area  of  the  wings  in  square  feet. 

The  second  term  represents  the  weight  of  fabric  in  above 
formulae.  In  Chapter  I.  we  saw  that  the  weight  of  the  wing 
structure  of  modern  machines  is  about  13  per  cent,  of  their 
total  weight.  This  figure  represents  the  best  that  has  been 
attained  in  practice  so  far,  and  is  the  result  of  much  careful 
attention  to  detail,  so  that  any  improvement  upon  it  will  not  be 
easy,  but  it  should  form  a  standard  of  reference  to  which  to  work. 

Stresses  due  to  Downloading.  —  In  normal  flight  the  re- 
sultant air  force  on  the  wings  acts  in  an  upward  direction, 
thereby  supporting  the  machine,  in  opposition  to  the  force  of 
gravity.  Under  certain  circumstances,  however,  the  pressure  on 
the  wings  may  be  reversed  in  direction,  as  for  instance  when  the 
elevator  is  depressed  and  the  machine  commences  to  dive.  The 
force  necessary  to  change  the  line  of  flight  of  the  machine 
depends  upon  the  radius  of  the  turn  with  which  the  machine 
commences  to  dive.  The  centrifugal  force  upon  the  machine 


The  reaction  to   this   force   must  be  provided   by  a  down 
pressure  on  the  wings.     For  example,  let 

P  =  force  on  wings. 
W  =  weight  of  machine. 
V  =  its  velocity. 
R  =  radius  of  flight  path. 

V3  /          V2  \ 

Then     P  -  W  -          -  =  W    i  -    —  ) 

j 


For  the  machine  referred  to  in  the  consideration  of  factors  of 
safety  (p.  143),  if  flying  at  100  m.p.h.  and  then  suddenly  directed 
downwards  on  a  path  of  radius  170  feet,  the  downloading  will  be 


=    1200      I     - 


i472 


=    1200  (l    -3'94)    =     -    2'94    X    1200 

or  the  downloading — indicated  by  the  negative  sign — is  about 
three  times  the  weight  of  the  machine. 


AEROPLANE    DESIGN 


The  effect  of  such  downloading  is  to  throw  the  down- 
bracing  wires,  which  are  shown  dotted  in  Fig.  122,  into  operation. 
A  further  instance  of  the  occurrence  of  downloading  stresses  is 
during  the  time  that  the  machine  is  resting  on  the  ground,  the 
downbracing  wires  then  being  loaded  by  the  weight  of  the  wing 
structure  itself. 

It  is  customary  to  design  the  wing  structure  for  down- 
loading on  the  assumption  that  the  down  forces  are  one-half  as 
great  as  the  maximum  lift  forces.  This  is  conveniently  ac- 
counted for  by  adopting  a  factor  of  safety  equal  to  one- half 
that  used  for  the  lift  forces. 

Investigation  of  the  stresses  set  up  in  the  drag  bracing  of  the 
wing  structure  will  be  dealt  with  later  in  this  chapter,  after  the 
questions  of  duplication  and  stagger  have  been  considered. 


FIG.   122. 

Stressing  of  the  Wing  Structure.— The  method  of  drawing 
the  stress  diagrams  for  the  external  bracing  system  of  an 
aeroplane  is  as  follows. 

The  method  adopted  is  similar  for  all  types  of  machines,  but 
as  the  biplane  is  the  type  in  most  general  use,  our  attention  will 
be  confined  to  this  type  of  structure  for  the  present.  The  general 
procedure  to  be  adopted  will  first  be  outlined,  and  then  an 
example  of  its  application  to  practice  will  be  given. 

(i.)  NORMAL  FLIGHT.— Let  the  total  weight  of  the  machine 
whose  wing  structure  is  to  be  designed  be  W,  and  let  w  be  the 
weight  of  the  wing  structure  alone.  Then  the  load  actually 
carried  by  the  structure  is  W  —  w,  since  the  wings  themselves  are 
directly  supported  by  the  air  pressure,  and  thus  relieve  the  struts 
and  wires  of  having  to  transmit  any  stresses  due  to  their  weight. 
The  air  pressure  is  transmitted  by  the  wing  fabric  to  the  ribs, 
which  in  turn  transmit  the  load  to  the  spars  which  are  braced  to 
the  body. 

An  aeroplane  being  symmetrical  about  its  longitudinal  axis, 
it  is  only  necessary  to  determine  the  stresses  due  to  half  the 
weight  on  one  side  of  the  machine.  Consider  a  biplane  as 
shown  in  Fig.  122.'  Let  T  be  the  area  of  top  plane  and  B  the 
area  of  lower  plane. 


DESIGN    OF   THE    WINGS  153 

We  must  first  determine  the  proportion  of  the  load  carried 
by  each  plane.  Owing  to  its  greater  area  and  also  to  biplane 
effect,  the  top  plane  will  carry  most  of  the  load.  Let  e  be  the 
biplane  coefficient,  taken  from  the  table  given  on  page  78,  for 
the  particular  ratio  of  gap/chord  used. 

(VV  -  w) 
Then  mean  pressure  over  top  plane  =  ,       -      ^ 

and  mean  pressure  over  lower  plane  =  P"  =  e  P' 
Therefore  load  on  top  plane      =  W  =  T  P' 
load  on  lower  plane  =  W"  =  B  P" 

The  variation  in  load  grading  at  the  wing  tips  known  as  'end 
effect '  must  now  be  taken  into  account.  We  shall  assume  the 
load  grading  over  the  outer  section  of  the  wing  to  be  parabolic. 
The  general  result  of  this  is  to  reduce  the  effective  area  of  the 


FIG.  123. 

planes.  For  this  reason  various  shapes  have  been  given  to  the 
wing  tips  in  the  endeavour  to  minimise  this  loss  as  much  as 
possible  ;  but  it  is  very  doubtful  if  these  special  shapes  are  worth 
the  extra  trouble  and  labour  involved  from  the  practical  point  of 
view.  Let  T'  and  B'  be  the  effective  areas  of  the  top  and 
bottom  planes  respectively,  obtained  from  T  and  B  by  sub- 
tracting the  area  lost  through  end  effect.  Then  we  have 

W 

Maximum  pressure  on  top  plane         =  — 

W" 

Maximum  pressure  on  bottom  plane  =  — — 

B 

The  curve  of  loading  along  the  span  can  now  be  set  out, 
since  it  is  the  product  of  the  pressure  per  square  foot  and  the 
chord  length  at  that  point.  Curves  for  both  the  top  and  bottom 
planes  must  of  course  be  drawn.  They  will  be  similar  in  nature 
to  Fig.  123. 

The  next  step  is  to. determine  the  reactions  at  the  supports. 
The  spars  approximate  very  closely  to  a  continuous  beam,  and 
consequently  the  determination  of  the  reactions  involves  the  use 
of  the  Theorem  of  Three  Moments  as  shown  at  D,  Table  XXII. 


154  AEROPLANE  DESIGN 

Graphical  methods  have  been  developed  for  determining  these 
reactions,  but  for  the  simple  loadings  usually  met  with  in 
aeronautical  practice  the  Theorem  of  Three  Moments  is  much 
quicker  and  simpler,  and  gives  results  which  are  quite  satis- 
factory. 

Let  wv  w2,  w^  etc.,  be  the  loading  per  foot  run  over  each 
bay,  determined  from  the  load  curve  previously  drawn. 

Considering  first  the  top  plane,  let  MA>  MB)  Mc>  &c.,  be  the 
bending  moments  at  A,  B,  c,  etc.  See  Fig.  123. 

The  bending  moment  at  A  is  due  to  a  varying  upward  load 
over  a  cantilever  of  length  Lp  and  must  be  determined  by  means 
of  graphic  integration  if  very  accurate  results  are  required.  If  the 
loading  diagram  be  assumed  parabolic  over  the  outer  section,  the' 
bending  moment  may  be  easily  calculated.  With  this  assump- 
tion, M  =  W-,  Lj  x  o .  4  Lj  where  Wx  is  the  average  loading  over 
this  span.  Then  bending  moments  at  B,  c,  D,  etc.,  are  deter- 
mined by  applying  the  theorem  of  three  moments. 

For  the  spans  A  B,  B  C,  we  have,  referring  to  Fig.  41, 
MA  L2  +  2  MB  (L2  +  L3)  +  Mc  L3  -  \  (w2  L23  +  0/3  L33)  =  o 

For  the  spans  B  C,  CD,  we  have,  by  a  further  application  of 
the  theorem, 

MB  L3  +  2  Mc  (L3  +  L4)  +  MD  L4  -  \  (w,  L8»  +  w,  L/)  -  o 

For  the  spans  c  D,  D  E,  by  a  further  application, 

Mc  L4  +  2  MD  (L4  +  L5)  +  ME  L5  -  I  K  L/  +  w5  V)  -  o 

Since  the  wing  span  is  symmetrical,  the  support  moment  at  D 
equals  the  support  moment  at  E,  and  the  support  moment  at  A  has 
previously  been  determined.  Hence  we  have  three  equations  to 
determine  the  three  unknown  moments  at  B,  C,  D.  These  can 
be  easily  obtained  by  successive  substitution  in  the  above 
equations. 

Knowing  the  bending  moments  at  the  supports,  it  is  now 
easy  to  determine  the  various  reactions  by  taking  moments. 

Let  RA,  RB,  Re,  &c.,  be  the  reactions.  Then  taking 
moments  about  B  for  the  reaction  at  A,  we  have 

W    T    2 

wl  Lj1  (o.  4  L!  +  L2)  +  — 2— 2-  -  RAL2  -  MB 


W.  L  2 
j  (o .  4  Lj  +  L.J)  +  -  -  M, 


or     RA 


DESIGN    OF   THE   WINGS  155 

Again  taking  moments  about  C  for  RB,  we  have 

(T  \         W    T    2 

_?  +  L  )  +      3    3 

-  RA(L2  +  L8)  -  R8L8  =  Mc 

Proceeding  in  this  manner  the  reaction  at  each  support  can  be 
obtained. 

The  formulae  look  somewhat  formidable,  but  their  application 
is  quite  simple,  and,  with  practice,  both  bending  moments  and 
reactions  can  be  determined  very  quickly.  The  application  of 
the  theorem  of  three  moments  as  used  above  assumes  that  the 
points  of  support  are  in  the  same  straight  line.  In  practice  this 
is  frequently  not  the  case,  the  most  notable  difference  being 
obtained  after  the  process  of  tuning-up.  Considerable  errors 
are  likely  to  be  introduced  in  this  manner,  and  if  it  is  impossible 
to  avoid  this  occurring  a  fresh  set  of  bending  moments  must  be 
obtained,  assuming  each  point  of  support  to  be  out  of  the 
straight  line  by  say  J" — this  will  produce  large  differences.  In 
this  case  the  more  general  form  of  the  theorem  of  three 
moments  must  be  used,  namely  : — 

6A2*_2  +  6^  +  MA^  +  2  MB  (^  +  ^  +  McLs 

^2  Ij3 

+  6  E  I  U— +  f-M  =  o     Formula  47 

\J-/2          -L'3  / 

where     A2,  A3  denote  areas  of  free  bending  moment  diagrams  over 

second  and  third  spans 

x.2  denotes  the  position  of  the  C.G.  of  A2  from  the  support  A 
xs  denotes  the  position  of  the  C.G.  of  A3  from  the  support  C 
£2  denotes  the  distance  of  B  below  A 
£3  denotes  the  distance  of  B  below  C 

A  further  proviso  in  the  application  of  this  theorem  is  that 
the  bracing  wires  are  attached  in  such  a  manner  that  the  re- 
actions pass  through  the  neutral  axis  of  the  spar.  In  practice 
this  is  not  always  easy  to  obtain,  and  in  such  cases  the  Bending 
Moment  diagrams  will  be  somewhat  modified. 

Having  determined  the  reactions  at  each  support,  the  stress 
diagrams  for  the  structure  considered  as  a  single  vertical  frame 
with  pin  joints  can  now  be  drawn  as  shown  in  Chapter  II.  An 
example  of  such  a  diagram  is  shown  in  Figs.  22  and  125. 

(ii.)  DOWNLOADING. — The  procedure  adopted  in  determining 
the  stresses  due  to  downloading  is  exactly  similar  to  that  out- 


156  AEROPLANE    DESIGN 

lined  above  for  normal  flight.     In  this  case  the  reactions  at  the 
points  of  support  will  be  downward. 

Reference  has  already  been  made  to  the  fact  that  it  is 
customary  to  design  the  wing  structure  for  downloading  forces 
of  one-half  those  obtained  in  normal  flight.  As  the  application 
of  the  centre  of  pressure  and  factor  of  safety  is  being  left  over 
until  the  question  of  detail  design  of  the  members-  is  being 
considered,  the  reactions  due  to  downloading  may  with  advan- 
tage be  set  out  equal  in  magnitude  but  opposite  in  direction  to 
the  lift  reactions.  The  stress  diagrams  for  downloading  can  now 
be  drawn.  It  must  be  remembered  in  this  case  that  it  is  the 
downbracing  wires  which  are  in  operation.  Fig.  126  illustrates 
a  downloading  stress  diagram. 

ILLUSTRATIVE  EXAMPLE.  —Before  proceeding  to  show  how 
to  determine  the  detailed  stresses  in  each  member  of  the  wing 
structure,  we  will  illustrate  the  methods  just  described  by  means 
of  a  practical  example,  and  draw  the  stress  diagrams  for  the 
external  bracing  of  the  biplane  shown  in  Fig.  124  (a)  and  (£). 
The  weight  of  the  machine  is  2000  Ibs.  and  the  weight  of  the 
wing  structure  is  300  Ibs.,  the  chord  of  the  wings  is  6  ft.,  span 
of  top  plane  40  ft.,  span  of  lower  plane  31  ft. 

AREA  OF  TOP  PLANE.  AREA  OF  BOTTOM  PLANE. 

Overhang  =      2\    x  6    =  13*5  Overhang  2  x  6  =  12 

AB  =      4      x  6    =  24  B'C'    =  39 

BC  =      6-5  x  6    =  39  C'D'  -  36 

CD  =      6      x  6    =  36 

IDE  =  J(2-S  x  6)  =     7'5 

120  87 

Distribution  of  load  over  upper  and  lower  planes  :  Upward  force 
to  be  distributed  =  2000  -  300  =  1700  Ibs. 

=    850  Ibs.  per  side. 

Biplane  effect :  The  ratio  of  gap/chord  is  unity,  hence  from  Table 
on  p.  78  the  factor  is  0*82 

850 

.*.  Average  pressure  top  plane  =  -  =  4-44  Ibs./sq.  ft. 

I2O   +     o2    X    07 

and  average  pressure  on  bottom  plane  =    0*82  x  4-5    =  3^67  Ibs./sq.  ft 
and  load  on  top  plane         =  4*44  x   120  =  532  Ibs. 
load  on  bottom  plane  =  3*67  x     87  =  318  Ibs. 

Total  =  850  Ibs. 


DESIGN    OF   THE   WINGS 


'57 


FIG.  1 


®   c;u  ®  D*kpr 

Line     D'agnum    of    t-Whinft  Sole 


-370 
-C40 

fSTo 
-KXO 
-WHO 


4-  lnjicar*sis  Tens 


FIGS.  124  to  126. — Method  of  setting-out  Stress  Diagrams. 


158  AEROPLANE    DESIGN 

Reduction  of  effective  area  due  to  end  effect.  Assuming  parabolic 
loading  over  the  outer  6  ft.  ( =  chord)  of  each  plane, 

The  equivalent  loss  in  area  =  6x6  x   '33  =  12  sq.  ft  ,  and 

hence  the  effective  area  of  the  top  plane  =  120-12  =  108  sq.  ft. 
arid  of  lower  plane  =     87  -  12  =     75  sq.  ft. 

.*.   Maximum  pressure  on  top  plane        =  — -  =  4/94,  say  5  Ibs./sq.  ft. 

I  Oo 

Maximum  pressure  on  bottom  plane  =  —  —  =4*25  Ibs./sq.  ft. 

The  loading  diagram  for  the  planes  can  now  be  drawn  as  in 
Fig.  124  (c)  (d),  since  load  per  foot  run  equals  pressure  at  that 
point  multiplied  by  the  width  of  the  chord,  which  in  this  example 
is  constant  and  equal  to  6  feet. 

Having  determined  the  load  distribution,  we  can  proceed  to 
find  the  Fixing  or  Support  Moments. 

From  Fig.  124  (c)  the  load  on  the  overhang  =  §  (2*25  x  30  x  '6)  =  27*0  Ibs. 

Bending  Moment  at  A  due  to  this  load       =  27*0  x  -f  x  2^25 

=  24-3  ft.  Ibs. 


Applying  Theorem  of  Three  Moments  to  the  spans  A  B,  B  c,  we  have 
4  MA  +  2  MB  (4  +  6-5)  +  Mc  (6-5)  -  1  (24-4  x  43  +  30  x  6'53)  =  o 

or  21  MB  +  6-5  Mc  =  2350        (i) 

For  the  spans  B  c,  CD,  we  have 

6-5  MB  +  2  Mc  (6-5  +  6)  +  6  MD  -  i  [30  (6-53  +  63)]  =  o 

or     6-5  MB  +  25  Mc  +  6  MD  =  3675        (2) 

For  the  spans  CD,  D  E,  we  have 

6  Mc  +  2  MD  (6  +  2-5)  +  2-5  ME  -  i  [30  (63  +  2-53)]  =  o 

or     6  Mc  +   17  MD  +  2-5  ME  =  1730        (3) 

From  symmetry  MD  =  ME 


=  c  

19-5 
Substituting  for  MD  in  (2)  we  have 

6-5  MB  +  25  Mc  +  532  -  1-85  Mc  =  3675 


DESIGN    OF   THE    WINGS  159 

Substituting  for  Mc  in  (i)  we  have 

r2I    MB    +    884    -    1-83   MB    =    2350 

or         i9'i7  MB  =  1466         .-.  MB  =  77  ft.  Ibs. 
Substituting  this  value  in  (5) 

=  3143  -jog   =  II4ft.lbs. 
23'15 

Substituting  this  value  in  (4) 

:  MD  =  !^f^-     54  ft.  Ibs. 

=  ME 

We  can  now  determine  the  Reactions. 
Taking  moments  about  B  for  RA 

27   {4  +  4  (2-25)}    +    100    X    2    -    4  RA    -    MB 

or  132  +  200  -  4  RA  =  77 

whence     RA  =  64  Ibs. 

Taking  moments  about  c  for  RB 

27  {4'9  +  6-5}  +  ioo  x  8-5  +  3^-_5)_  _  IO-5  RA  -  6-5  RB  =MC 

or  308  +  850  +  634  -  672  -  6-5  RB  =   114 

whence     RB  =  155  Ibs. 

Taking  moments  about  D  for  Rc 

30  x  62 
27  (11*4  +  6)  +  ioo  x  14-5  +  30  x  6'5  x  9^25  +  - 

-  16-5  RA  -   [2-5  RB  -  6  Rc  =  MD 

or  470  +  1450  +  1800  +  540  -  1050  -  1940  -  6  Rc  =  54 

whence     Rc  =  202  Ibs. 

Taking  moments  about  E  for  RD 

27  (i7'4  +  2-5)  +  ioo  x  17  +  30  x  6*5  x  11*75  +  I^°  x  5'5 

+  - --^-^  -  19  RA  -  15  RB  -  8-5  Rc  -  2-5  RD  =ME 

or  53^  +  1700  +  2290  +  990  +  94  -  1215  -  2330 

-  1720  -  2-5  RD  =  54 
whence     RD  =  115  Ibs. 

Sum  total  of  Reactions  =  64  +  155  +  202  +  115  =  536  Ibs. 

The  load  on  the  top  plane  was  found  to  be  532  Ibs.  The 
slight  difference  is  due  to  the  fact  that  the  loading  was  taken  at 
5  Ibs.  per  square  foot  instead  of  the  more  accurate  figure  of 


160  AEROPLANE    DESIGN 

4-94  Ibs.  per  square  foot.     The  total  sum  of  the  reactions  should 
always  be  checked  in  this  manner. 

In  a  similar  manner  the  fixing  moments  and  reactions  at  the 
lower  plane  supports  can  be  determined.  It  should  be  noted 
that  there  are  no  lift  forces  over  the  portion  D'E',  .which  repre- 
sents the  base  of  the  fuselage.  The  reactions  are  : 

RB'  «  78  Ibs. ;  RC'  «  176  Ibs. ;  RD<  -  62  Ibs. 

The  vertical  reactions  due  to  the  lift  forces  being  known,  the 
next  step  is  to  draw  the  stress  diagrams  on  the  assumption  that 
the  frame  is  pin-jointed.  The  front  elevation  of  the  machine  is 
set  out  to  scale,  and  the  stress  diagram  for  the  lift  forces  drawn 
in  the  usual  manner,  as  shown  in  Fig.  125.  In  some  cases  it 
may  be  found  more  convenient  to  draw  a  diagram  for  both  front 
and  rear  frames  separately,  by  applying  the  requisite  C.P.  factor 
to  give  the  maximum  loading  on  each  ;  but  in  this  example  a 
single  diagram  will  suffice,  and  the  stresses  in  each  frame  can 
be  determined  by  applying  the  correct  coefficients  afterwards. 
Having  completed  the  diagram,  the  stresses  in  each  member  due 
to  the  lift  forces  in  horizontal  flight  should  be  tabulated. 

The  stress  diagram  for  the  downloading  forces  is  shown  in 
Fig.  126. 

General  Procedure  for  Design  of  the  Members  of  the 
Wing  Structure. — From  the  stress  diagrams  of  the  machine, 
considered  as  a  single  vertical  frame  and  with  a  loading  on 
the  wings  equal  to  its  weight,  the  actual  loads  in  the  various 
members — upon  which  .  their  design  is,  of  course,  based — are 
determined  by  applying  the  necessary  centre  of  pressure  coeffi- 
cients and  the  requisite  factor  of  safety.  For  all  front-frame 
members  of  the  wing  structure  the  maximum  stresses  will  be 
incurred  with  the  most  forward  position  of  the  centre  of 
pressure  during  flight,  and  the  maximum  stresses  in  the  members 
of  the  rear  frame  of  the  wing  structure  will  be  incurred  with  the 
most  backward  position  of  the  centre  of  pressure  during  flight. 
As  will  be  seen  later,  however,  this  condition  of  affairs  may  be 
modified  by  the  method  of  duplication  which  is  employed.  By 
reference  to  the  characteristics  of  the  aerofoil  which  has  been 
selected  the  travel  of  the  C.P.  is  known,  and  hence  the  maximum 
proportion  of  the  load  which  can  fall  on  either  front  or  rear 
frame  can  at  once  be  determined  in  the  manner  shown  on 
page  149, 

As  the  factor  of  safety  to  be  adopted  is  complicated  by  the 
method  of  duplication  employed,  this  question  will  now  be 
considered. 


DESIGN   OF   THE   WINGS 


161 


DUPLICATION  OF  THE  EXTERNAL  WING  BRACING. — The 
possibility  of  having  one  or  other  of  the  wing-bracing  members 
shot  away,  or  otherwise  rendered  inoperative  in  flight,  makes 
it  necessary  to  consider  this  eventuality  when  designing  a 
machine.  In  certain  cases  it  is  desirable  to  provide  an  alterna- 
tive path  whereby  the  lift  reactions  on  the  wing  may  be  trans- 
ferred to  the  body.  Such  duplication  provides  an  additional 
safeguard  against  the  failure  of  a  bracing  wire  or  fitting  due  to 
faulty  material  or  bad  workmanship.  Two  methods  of  dupli- 
cation are  in  general  use  : — 

I.  Direct  duplication,  in  which  method  two  wires  are  inserted 
one  behind  the  other ;  and  each  one  capable  of  taking  two-thirds  of 
the  maximum  load  likely  to  fall  on  this  member.  In  the  event 
of  one  wire  failing,  the  other  wire  will  transmit  the  load  ;  but  the 
system  would  now  have  a  factor  of  safety  of  only  two-thirds  that 


FIG.  127. — Transmission  of  Forces  in  Biplane  Truss 
with  Broken  Wire. 


of  its  previous  value.  In  large  machines  these  two  wires  should 
be  faired  off  to  an  approximate  streamline  shape,  in  order  to 
keep  down  the  resistance,  which  would  otherwise  be  consider- 
ably increased. 

2.  Duplication  through  the  Incidence  Bracing. — In  this  method 
the.  load  originally  carried  by  the  broken  wire  is  transmitted 
through  the  incidence  wire  to  the  corresponding  unbroken  frame, 
and  from  thence  to  the  body.  Reference  to  Fig.  127  will  make 
this  method  clear.  Suppose,  for  example,  that  the  lift  wire 
C  D'  is  broken.  Originally  this  wire  was  transmitting  the  lift 
reactions  at  A,  B,  B',  C,  c',  down  to  the  body  at  D'.  After  it  is 
broken  these  reactions  are  carried  by  the  incidence  wire  C  c' 
down  to  the  point  C/,  whence  they  are  transmitted  up  the  rear 
strut  Cx  c/,  and  thence  by  way  of  the  rear  lift  wire  Cx  D/  down 
to  the  body.  In  a  similar  manner  if  the  rear  wire  Cx  D/  be 
broken,  then  the  load  previously  carried  by  this  wire  is  trans- 
mitted by  the  incidence  wire  q  c'  to  the  point  c',  and  thence  by 


AEROPLANE    DESIGN 

way  of  the  front  strut  and  lift  wire  down  to  the  body  at  the 
point  D'.  Since  it  is  possible  for  any  one  of  the  external 
bracing  wires,  either  '  lift '  or  '  down,'  to  be  put  out  of  action,  it 
is  necessary  to  consider  the  case  of  each  wire  separately  and  to 
examine  what  effect  will  be  produced  upon  the  remaining 
members  of  the  structure  in  each  contingency.  The  factor  of 
safety  with  one  wire  broken  is  generally  taken  as  two-thirds 
that  when  all  the  wires  are  intact.  From  the  diagram  it  is  clear 
that  the  main  bracing,  incidence  bracing,  and  drag  bracing  are 
all  affected,  so  each  will  be  considered  in  turn. 

(a)  Effect  on  the  Main  Bracing. — It  has  already  been  shown 
that  in  the  event  of  the   lift  wire  c  D'  being   broken    the  lift 
reactions  in  the  previous  bays  of  the  front  frame  will  be  trans- 
mitted to  the  rear  frame  by  the  incidence  wire.     This  will  result 
in   a  much  greater  load  on  the  rear  strut  cx  C/  the  increased 
load   being  the  sum   of  these    reactions.     The   value   of  these 
reactions,  however,  depends  upon. the  position  of  the  centre  of 
pressure  of  the  air  forces,  and  thus  there  are  three  cases  to  be 
considered  in  the  design  of  wing  structures  when  this  method 
of  duplication  is  adopted.     For  the  biplane  truss  illustrated  in 
Fig.  127  these  cases  are  : — 

i.  With  the  C.P.  forward  and  reduced  factor  of  safety. 

ii.  With  the  C.P.  rearward  and  reduced  factor  of  safety. 

iii.  With  the  C.P.  rearward,  the  structure  intact,  and  the 
maximum  factor  of  safety. 

In  case  (ii.)  the  load  transferred  from  the  front  frame  will  be 
less  than  in  case  (i.),  but  the  loads  due  to  the  outer  lift  reactions 
on  the  back  frame  will  be  greater  than  in  case  (i.).  Moreover, 
the  reduced  factor  of  safety  used  in  the  first  two  cases  may  lead 
to  the  conditions  of  case  (iii.)  being  the  criteria  to  adopt  for 
design,  and  only  a  numerical  determination  will  establish  which 
condition  produces  the  maximum  stress  in  the  strut  and  wire. 
The  problem  is  not  a  difficult  one,  though  somewhat  more  involved 
than  that  obtained  when  direct  duplication  is  employed.  The 
example  given  later  in  this  chapter  will  help  to  clear  up  any 
difficulties. 

(b)  Effect  on  the  Incidence  Bracing. — When  the  wing  struc- 
ture is  intact  there  are  no  stresses  in  the  incidence  bracing  due 
to  air  forces.    Their  function  under  such  conditions  is  principally 
to  make  the  structure  rigid.    With  one  of  the  main  bracing  wires 
broken,  however,  the  corresponding  incidence  wire  is  called  upon 
to  carry  its  load  and  it   must   therefore  be  designed   for   this 
purpose.     The  load  in  the  incidence  wire  will  be  the  sum  of  the 
reactions  in  the  frame  to  the  left  of  the  broken  wire  resolved  in 
its  direction.     For  example,  if  ab  (Fig.  128)  represent  the  sum 


DESIGN   OF   THE   WINGS 


163 


of  such  reactions,  then  b  c  will  represent  the  corresponding  stress 
in  the  incidence  wire.  The  horizontal  component  a  c  of  tension 
in  the  incidence  wire  is  taken  by  the  drag  bracing  which  must 
now  be  considered. 

(c)  Drag  Bracing. — The  general  form  of  the  wing -drag 
bracing  is  shown  in  Figs.  108,  139. 

It  is  general  practice  to  assume  the  maximum  drag  force  to- 
be  uniformly  distributed  on  the  wings  of  a  machine,  and  to  be 
equal  to  one-seventh  of  its  total  weight,  and  to  design  on  this 
basis.  Here  again  the  method  of  duplicating  the  lift  and  down 
bracing  wires  will  largely  influence  the  design.  With  the  in- 
cidence wires  in  operation,  there  will  be  a  component  of  their 
tension  acting  in  the  plane  of  the  drag  bracing,  and  hence  this 
must  be  sufficiently  strong  to  transmit  the  resulting  shear  along 
to  the  centre  section.  The  simplest  method  of  determining  the 
stresses  in  the  drag  bracing  will  be  to  draw  the  stress  diagram, 


FIG.  128. 

applying  the  forces  due  to  the  incidence  bracing  at  the  correct 
points  of  application.  Referring  to  Fig.  127,  if  we  suppose  the 
front  lift  wire  B  c'  to  be  broken,  and  the  incidence  wire  B  B/  to  be 
transmitting  the  lift  forces  from  the  front  to  the  rear  frame  :  the 
resulting  tension  in  B  B/  will  cause  an  unbalanced  force  in  the 
direction  of  the  arrow,  and  the  frame  would  therefore  become 
distorted  unless  some  means  were  provided  to  counteract  this 
force.  The  drag  bracing  wire  B1^  offers  the  best  means  of 
providing  the  necessary  reaction  and  the  shear  will  be  trans- 
mitted along  the  path  indicated  by  the  arrows.  The  stresses  set 
up  in  the  drag  bracing  in  this  manner  will  be  very  much  greater 
than  those  due  to  the  drag  forces  alone,  and  the  drag  bracing 
will  therefore  need  to  be  made  correspondingly  stronger. 

Change  of  Direction  of  Drag  Forces  in  the  Wing 
Structure. — At  first  sight  it  would  appear  that  the  component 
of  the  drag  forces  in  a  wing  structure  always  acted  from  the 
front  to  the  rear  of  the  wing.  This,  however,  is  not  the  case,  as 


164  AEROPLANE   DESIGN 

was  pointed  out  on  p.  60.  The  following  example  further  illus- 
trates this  effect  as  influenced  by  the  resistance  of  the  bracing 
wires. 

From  the  R.A.F.  6  aerofoil  characteristics  we  find  that  the 
ratio  L/D  at  12°  angle  of  incidence  is  11.  Making  an  allow- 
ance for  the  resistance  of  the  bracing  wires,  this  ratio  will  be 
taken  as  10.  Next  set  out  the  values  of  the  lift  and  drag 
perpendicular  and  parallel  to  the  air  stream  respectively. 
From  Fig.  45  it  will  be  seen  that  the  resultant  force  on 
the  section  is  forward  of  the  normal  to  the  chord  line.  For 
such  an  attitude  of  the  wings,  therefore,  the  component  of  the 
drag  forces  is  acting  in  a  forward  direction.  For  the  purposes 
of  design  work  it  is  best  to  assume  that  the  drag  forces  act  in 
such  a  direction  that  they  cause  the  greatest  stress  in  the  spars. 


FIG.  129. 

A  moment's  consideration  will  show  that  for  the  back  spar 
design  the  drag  forces  should  be  acting  in  the  direction  shown 
in  Fig.  127,  and  that  for  the  front  spar  they  should  act  in  the 
opposite  direction.  This  is  because  the  spars  are  almost  in- 
variably designed  to  resist  compression,  and  consequently  the 
drag  forces  should  act  in  such  a  manner  as  to  increase  this 
compression. 

Stagger. — The  effect  of  stagger  upon  the  stresses  set  up  in  a 
wing  structure  is  to  introduce  another  factor  to  be  applied  to 
the  loads  obtained  from  the  stress  diagram  of  the  vertical  frame 
already  discussed.  Reference  to  Fig.  129  will  make  this  clear. 
It  will  be  seen  from  this  figure  that  the  vertical  reaction  of  the 
lift  forces  is  resisted  by  the  lift  bracing,  which  is  inclined  at  an 
angle  6  to  the  vertical.  As  a  result  of  this  the  stresses  obtained 
from  the  diagram  for  the  vertical  frame  bracing  must  be 
multiplied  by  the  factor  i/cos  6  for  the  case  of  the  staggered 
machine. 


DESIGN   OF  THE   WINGS 


165 


Moreover,  it  will  be  apparent  that,  on  account  of  the  line  of 
pull  of  the  lift  wires  not  being  in  the  same  plane  as  that  of.  the 
lift  forces,  there  will  result  a  horizontal  component  of  the  lift  in 
the  direction  of  the  drag  bracing  =  L  tan  0,  where  L  is  the  lift 
reaction  at  the  joint  considered  ;  and  the  drag  bracing  must 
therefore  be  sufficiently  strong  to  transmit  the  shear  resulting 
from  these  horizontal  components  in  addition  to  that  due  to  the 
ordinary  drag  forces.  This  is  illustrated  in  Fig.  129  (a). 

Similarly  at  the  lower  plane  joints  the  lift  reaction  is  trans- 
mitted by  means  of  the  inclined  strut  to  the  top  joint  where  the 
lift  wire  is  attached.  Hence  the  stress  in  the  struts  obtained 
from  the  vertical  frame  diagram  must  also  be  multiplied  by  the 
factor  i /cos  6.  Also  there  will  be  a  backward  component 
=  L'  tan  9  to  be  taken  by  the  lower  plane  drag  bracing  where 


Reaction* 


FIG.  129  (a). 


\L 


FIG.  129  (b). 


L'   is   the   lift  reaction    at   any   lower  plane  point  of  support. 
(See  Fig.   129  (£).) 

The  method  of  determining  the  stresses  in  the  wing  structure 
of  a  staggered  machine  may  therefore  be  summarised  as 
follows  : — 

(i)  Lift  Bracing  and  Interplane  Struts. — Multiply  the  loads 
obtained  from  the  vertical  stress  diagram  by  the  factor where 

6  is  given  by  the  relationship  tan  0  =  Stagger 

gap 

(ii)  Drag  Bracing. — To  the  ordinary  drag  loads  due  to 
resultant  air  forces  add  a  component  equal  to  L  tan  6  at  each 
point  of  attachment  of  wing  bracing,  where  L  is  the  reaction  at 
the  joint  considered,  and  draw  stress  diagrams  for  combined 
reactions.  An  example  of  this  is  shown  in  Fig.  146., 

It   should  be  noted    that   in   the  case  of  the   downloading 


166  AEROPLANE    DESIGN 

forces  on  a  staggered  machine  the  downbracing  loads  must  be 
multiplied  by  the  factor  I/cos  0,  while  the  horizontal  component 
in  the  direction  of  the  drag  bracing  will  act  in  the  opposite  direc- 
tion to  that  when  the  lift  wires  are  in  operation.  A  separate 
stress  diagram  for  drag  bracing  of  a  staggered  machine  must 
therefore  be  drawn  for  downloading  conditions. 

Detail  Design  of  the  Wing  Structure. — The  various  cases 
likely  to  be  met  with  in  stressing  a  wing  structure  having  been 
considered,  the  detail  design  of  the  various  members  can  be 
investigated.  From  the  previous  paragraph  we  see  that  the 
actual  maximum  loads  for  which  it  is  necessary  to  design  each 
member  can  be  obtained  by  applying  : 

(#)  The  requisite  C.P.  coefficient ; 

(b)  The  necessary  factor  of  safety  ;  and 

(c)  Stagger  coefficient  in  the  case  of  a  staggered  machine,  to 

the  load  obtained  from  the  stress  diagram  drawn  for 
unit  load. 

These  detail  members  comprise  : 

1.  The  lift  and  down  bracing,  j 

2.  The  incidence  bracing.         J        Bracing. 

3.  The  interplane  struts. 

4.  The  drag  struts  and  drag  bracing. 

5.  The  spars. 

The  External  Bracing.— The  most  common  method  of 
bracing  the  wing  structure  is  by  means  of  high  tensile  stream- 
line wires  or  rafwires,  of  which  particulars  are  given  in  Table 
XXVI. 

These  wires  are  rolled  out  of  circular  section,  down  to  the 
shape  shown  in  Fig.  130  (a)  and  (£),  by  means  of  specially 
shaped  rollers,  the  process  being  termed  '  swaging/  This 
process  has  the  effect  of  making  the  steel  very  brittle,  and  also 
sets  up  initial  strains  in  the  material.  It  is  therefore  necessary 
to  subject  the  wires  to  heat  treatment,  which  consists  of  placing 
them  in  a  bath  of  molten  lead  or  in  boiling  salt  solution,  where 
they  are  allowed  to  remain  until  they  have  acquired  the  uniform 
temperature  of  the  bath,  after  which  they  are  removed  and 
allowed  to  cool  slowly.  Previous  to  this  heat  treatment  the 
yield  point  and  the  ultimate  stress  point  are  practically  coin- 
cident, and  there  is  no  appreciable  extension  before  fracture. 
The  breaking  stress  of  the  wire  in  this  condition  is  very  often  in 
the  neighbourhood  of  100  tons  per  square  inch.  After  heat 
treatment  the  yield  and  ultimate  stress  points  are  much  reduced, 


DESIGN    OF   THE   WINGS 


167 


the  latter  being  about  70  tons  per  square  inch  ;  but  there  is  now 
an  extension  of  from  15%  to  2Q°/Q  on  a  gauge  length  of  8". 

TABLE  XXVI. 


SIZE 

RAFW1RES 

TIE  RODS 

TENSILE 
STRENGTH 

DiAof~Thn=ad 

L.H.  or  R.H. 

LentfhofTfesd 

Section    of       ^^ 
Sl-neamline 

Dia   of  Rod 
(circular) 

Ibs 

Major  Axis 

Mirvar  AKIS 

4BA 

1  0" 

0-17" 

0-06* 

o-io' 

•1050 

2  B.A 

\  1" 

0-18" 

0-07" 

O-I35 

190O 

W  B.5.F 

1-3" 

0-4" 

0-09' 

o-ise' 

3450 

%2      " 

1-4" 

0-47" 

o-io" 

0211" 

4650 

?I6     " 

1    5* 

0-50" 

o-ir 

0-234" 

5700 

%Z     ' 

1-6" 

0-57" 

0-13" 

0262" 

7150 

%"      " 

1  7- 

0-60* 

014" 

0-285  " 

8500 

%2     *' 

1-8* 

073" 

0-15" 

0-310" 

10250 

'5/*     . 
/32    * 

1  9" 

075" 
078" 

0-16" 
0-17" 

0-340" 
0360" 

11800 
13800 

Xa     " 

2-0" 

O-80" 

0-18" 

0-380' 

15500 

(a)         RaPwir»«  wil'h   Universal   Fork  Joinh 


(b)         Rafwir»c   wil-h    Plain    Fork  Joinf. 


(c)        Tic-Rod  wifh    Plain  Fork  Joinf. 

FIG.  130. — Bracing  Wires  and  Tie-rods. 

The   ends   of  the   wires  are   left   circular,    and    are   finally 
screwed   with  right-  and  left-hand   threads  respectively,  which 


i68 


AEROPLANE   DESIGN 


screw  into  plain  or  universal  fork  joints  as  shown  in  Fig.  130  (a) 
and  (&).  These  fork  joints  are  in  turn  pin-jointed  to  the  wiring 
plates  at  the  points  of  attachment  to  the  wing  structure. 

Another  method  of  external  bracing  is  by  means  of  stranded 
wires.  The  strands  manufactured  by  Messrs.  Bruntons,  of 
Musselburgh,  are  illustrated  in  Fig.  131  :  a  is  a  section  which 
should  be  used  only  in  those  places  where  little  wear  takes 
place.  These  strands  combine  strength  and  flexibility,  and  can 
be  obtained  in  any  required  size.  They  do  not  deteriorate  so 
rapidly  as  a  rafwire,  because  in  the  latter  type  of  bracing  there 
is  a  certain  amount  of  crystallisation  due  to  the  vibration. 
Further,  if  a  single  tie-rod  has  a.  slight  nick  upon  its  surface 


(c) 


7  Srpands, 
each  7  Wires. 


7Sl-pands, 
each  19  Wires 


FIG.  131. — Bracing  Cables  (Brunton's). 

it  is  liable  to  snap  under  a  sudden  accidental,  but  not  necessarily 
severe,  strain.  In  the  case  of  a  strand  such  a  nick  would  mean 
the  severance  of  one  or  two  wires  only,  and  would  not  greatly 
impair  the  strength  of  the  complete  strand. 

Table    XXVII.    gives    some    details    relating   to   the   sizes, 
weights,  and  strength  of  the  strands  illustrated  in  Fig.  131. 


TABLE  XXVII. — PARTICULARS  OF  STRANDS  FOR  AIRCRAFT 
PURPOSES. 


Size. 

Circumference 
in  inches. 


I'O 


Weight  per 

100  feet. 

Ibs. 


3*33 

5*5 

8-0 
12-5 
16-66 


Breaking 

strength. 

Ibs. 

784 

1332 
1904 
2576 

5I52 

7056 
10080 


DESIGN    OF   THE    WINGS 


169 


These  strands  are  tightened  by  the  insertion  of  strainers  or 
turnbuckles,  a  standard  type  of  which  is  shown  in  Fig.  132. 
Details  of  these  turnbuckles  are  incorporated  in  Table  XXVIII. 

An  illustration  of  their  use  is  given  in  Fig.  138  at  q,  r,  s.*jjfln 
general  the  barrel  portion  is  made  of  gun-metal,  and  the  eye  and 
fork  portions  of  steel. 

TABLE  XXVIIL— STRAINERS. 


WASHER 


FORK    A 


FORK  A. 


Diam.  of 
Thread. 

Dimensions. 

A. 

B. 

C. 

D. 

E. 

F. 

G. 

H. 

J. 

K 

L. 

M. 

Tolerances. 

+  '015 

-  0. 

+  '04 

-  0. 

+  •04 
—  o. 

+  -OC2 
—  'OO2. 

+  '015 
—  o. 

+  '015 
-  o. 

+  '015 

-  0. 

+  001 

-  o. 

+  015 
-  o. 

Min. 

B.S.F. 

Strength. 

Ins. 

Ins.      Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

i 

95      cwt. 

i  '5 

1-6       i'o 

i 

•418 

i  '08        '7 

"3 

•07 

'54 

'5 

'2 

A 

72        ). 

1  4 

i'5         '875 

7e 

•365 

'95 

•65 

'25 

•06 

'475 

•438 

'2 

i 

52 

I  '2 

i  '3         "75 

i 

'30Q 

•8 

'55 

•2 

•06 

*4 

'375 

'2 

A 

34 

I'O 

I  '2             '65 

A 

"252 

'7 

'475 

*2 

•05 

'35 

•312 

'2 

A 

29 

'9 

I  'I             '60 

A 

•23           '65 

'45 

'2 

*°4 

•325 

•281 

"2 

i 

2I'5        ,, 

•8 

I'l 

•5 

i 

•20           '56 

•42 

*2 

•04 

•28 

•250 

'2 

zBA 

«'S     ii 

'7 

I  'I 

'4 

2  BA 

•i47         '43 

'31 

'IS 

•04 

•215 

•187 

'2 

4BA 

6'7     „ 

•6 

1.0 

'35 

4BA 

*n 

•38 

•26 

'12 

•04 

'19 

•156 

'2 

Diam.  of 

Dimensions. 

N. 

O. 

P. 

Q. 

R. 

s. 

T. 

U.      V. 

W.      X. 

Y. 

IZ. 

Thread 

- 

i                 ;  '! 



Tolerances. 

+  -oi 

+  01 

+  0 

+  '015 

+  -OI!+'OI 

-  o. 

-  0. 

-'001. 

-  o. 

-      0.               -     0.        ; 

Min. 

Strength. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins.     Ins. 

Ins.  i  Ins. 

Ins. 

Ins. 

i 

95      cwt. 

•25 

'17 

•96 

•86 

•498 

•64 

'05 

,     1-08 

i 

A 

i 

A 

A 

72         ,, 

*2 

•16 

'91 

•8 

•436 

•56 

'05 

'I         j       "07 

7* 

A 

H 

*V 

f 

52         i, 

'2 

•16 

'9 

'7 

'373 

•52 

'025 

'I                -07 

i 

& 

i 

A 

A 

34         ,, 

'IS 

'15 

'71 

'59 

'310 

'41 

•025 

"07  !   '05 

A 

A 

*    l  A 

A 

29         » 

*I 

**4 

•68 

•56 

•279 

'38 

•025 

•07     -05 

A 

A 

f      A 

i 

«'5     ii 

•075 

-I4 

•65 

'53 

•248 

*35 

•025 

•o7  ;  -05 

i 

A 

f  . 

A 

2BA 

"'5     „ 

•075 

.14 

'53 

'42 

•185 

'3 

•025 

•»7       '05 

A 

iV 

J 

A 

3BA 

6'       ,, 

•07 

"M 

•48 

'37 

'154 

•245 

•025 

•07    -05 

A 

A 

i 

A 

170 


AEROPLANE   DESIGN 

30° 


Riht-  or-  Left   Hand 


All   holes   must  not'  be  moce    than  -01 
off    <fc_   of    rupnbuckle-. 

EYEttC". 


BARREL  B. 


Dimensions. 

A. 

B. 

C. 

D. 

E. 

F. 

G. 

H. 

J. 

K. 

L. 

Tolerances. 

+  •08 
-  o. 

+  0 

-  '04. 

+  •04 

—  o. 

+  '015 
—  o. 

+  '015 
-  o. 

+  •015 
-  o. 

Diam.  of 

B.S.F. 

thread. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

i 

5  '75 

I'O 

2  '35 

i 

•6  1 

'75 

H 

'25 

•07 

'73 

I'O 

iV 

S'*5 

•875 

2'I 

A 

'54 

•6 

U 

•2 

•06 

.'64 

•86 

i 

4'5 

"75 

1-8 

i 

'45 

*55 

i? 

'2 

'05 

'55 

•78 

'A 

4'i 

•65 

1-6 

A 

'37 

'5 

U 

•15 

•°5 

'45 

•64 

A 

3  '7 

•6 

i  '45 

A 

'35 

*45 

1% 

•i 

•05 

•42 

•60 

i 

3  '5 

'5 

i*4 

i 

'3 

'4 

A 

•075 

3?S 

•36 

'5a 

2BA 

3'3 

'4 

i  '4 

2BA 

'23 

'3 

7 
3? 

•075 

'«5 

•28 

'45 

4BA 

3'° 

'35 

1-28 

4BA 

'2 

'24 

A" 

•075 

'°5 

"25 

'37 

EYE  C. 


Dimensions. 

A. 

B. 

C. 

D. 

E. 

F. 

G. 

H.         J. 

K. 

L. 

M. 

Tolerances. 

+  '015 

-  0. 

+  '04 
—  o. 

+  •04 

—  o. 

+  002 
-   002. 

+  '015 

-  0. 

+  '015 
-  o. 

+  '015 
—  o. 

+  '015 
-  o. 

Diam.  of 

B.S.F. 

thread. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins.      Ins. 

Ins. 

Ins. 

Ins. 

i 

k*b 

•6 

I'O 

i 

'418 

i'i 

'55 

'25     «  *«>7 

'55 

'275 

•40 

I7o 

'9 

'5 

•875 

fe 

'365 

'96 

'48 

•2          '06 

•48 

•24 

'35 

1 

•8 

'3 

'75 

i 

'3°9 

•82 

'4i 

•2          '06 

'4i 

•205 

'30 

A 

•65 

•2 

'65 

A 

'252 

•68 

'34 

'i5         '05 

'37 

'17 

'25 

A 

'55 

•i 

'6 

A 

'23 

'58 

•29 

•i           '04 

•29 

'MS 

•225 

1 

'5 

'i 

*5 

i 

•20 

'50 

'23 

'075       '04 

<25 

'US 

"20 

2  BA 

'45 

'i 

'4 

2BA 

•i47 

•40 

•X9 

*°75       '04 

*2 

'095 

<I[5 

4BA 

'45 

'0 

'35 

4BA 

'ii 

•40 

'19 

•07        '04 

*2 

'095 

'i5 

FIG.  132. — Complete  Strainers. 


Forked    one    end . 


Double  eye. 


DESIGN    OF   THE   WINGS 


.17.1 


The  Interplane  Struts. — Investigations  have  been  carried 
out  in  order  to  determine  the  best  shape  of  strut  for  aeronautical 
work,  and  an  account  of  some  of  these  experiments  will  be  given 
in  Chapter  VI.  The  essential  features  of  such  a  strut  are  low 
resistance  and  small  variation  of  resistance  with  change  of  angle 
of  yaw  of  the  machine.  The  researches  have  shown  that  the 
nose  of  the  strut  should  not  be  too  blunt,  while  the  rear  portion 
may  be  given  an  almost  straight  taper  from  the  point  of 
maximum  thickness  at  about  one-third  the  length  of  the  strut 
from  the  leading  edge,  right  down  to  the  rear  or  trailing  edge. 

The  type  of  strut  most  frequently  met  with  in  practice  at  the 
present  time  is  the  solid  streamline  spruce  strut  tapering  from  a 
maximum  section  at  the  centre  of  its  length  down  to  both  of  its 
ends.  With  large  machines  considerations  of  weight  make  it 
necessary  that  these  struts  should  be  made  hollow,  or  that 


(b) 


Solid    Wooden  Strut 
up      of 


Hollow   Wooden   Strut- 
covered   wiMi    fabric 


FIG.  133. — Types  of  Strut  Sections. 

an  alternative  form  of  construction  should  be  adopted.  This 
alternative  form  may  consist  of  a  steel  circular  tube  faired  to  a 
streamline  shape  by  means  of  three-ply  wood — see  Fig.  133  (#)— 
or  a  built-up  section  secured  by  glue  and  fabric — see  Fig.  133  (c). 
Steel  struts  have  also  been  designed,  and  Fig.  1 33(^0  shows 
such  a  strut.  It  is  composed  of  three  units,  produced  entirely  by 
mechanical  processes,  the  second  diaphragm  being  added  to  give 
greater  rigidity  and  strength.  The  units  are  blanked  out  and 
formed  in  presses,  and  then  united  by  spot  welding.  The  total 
weight  ^  is  3-15  Ibs.,  against  3-25  Ibs.  for  a  wooden  strut;  while 
the  failing  load  is  77  tons,  against  -475  tons  for  a  wooden  strut. 
The  design  of  a  tapered  strut  is  a  matter  requiring  con- 
siderable care,  for  unless  the  correct  taper  is  used  throughout, 
the  strength  of  the  strut  may  be  considerably  reduced,  so  that 
the  final  result  would  be  much  worse  than  using  a  parallel  strut. 


172 


AEROPLANE    DESIGN 


With  the  correct  taper,  it  is  possible  to  obtain  a  reduction  in 
weight  of  13%,  and  a  reduction  in  resistance  of  8%  over  the 
parallel  strut  of  the  same  strength.  A  theory  for  the  design  of 


Reproduced  by  courtesy  of  '  Flight.' 

FIG.  134(0). — Analytical  Sketch  of  Interphne  Strut  Attachment,  Lift 
Wire  Attachment,  Internal  Drag  Bracing,  and  Drag  Strut. 


DESIGN    OF   THE   WINGS 


173 


such  struts  which  has  been  found  to  give  good  results  in  practice 
has  been  developed  by  Messrs.  Barling  and  Webb,  and  an  account 
is  given  in  the  Aeronautical  Journal  for  October,  1918.  As  it 


TYPES  OF  STRUT  FITTINGS. 

{Reproduced  by  courtesy  of  *"  Flight ?} 


FIG.  1 34  (J). 


FIG.  134(4 


FIG.  134  (d}.— Sketch  showing  Attachment  of  Interplane  Strut 
and  Drag  Strut  to  Main  Spar. 

seems  probable  that  this  theory  will  be  considerably  used  in  the 
future  design  of  tapered  struts,  the  main  outlines  of  this  theory 
are  included  here,  and  later  on  in  this  chapter  an  example  is 
given  showing  how  to  manipulate  the  complicated-looking 


AEROPLANE    DESIGN 


equation  in  actual  practice.     It  should  be  noted  that  the  theory 
holds  for  struts  of  any  regular  cross  section  in  which  a  curve  can 

be  drawn  connecting  the  Moment  of 
Inertia  with  thickness. 

Tapered  Strut  Formula. — Deri- 
vation of  Expression  for  the  Meridian 
Curve.  —  The  strut  is  assumed  to 
have  frictionless  pin -joints.  It  de- 
flects under  an  end  load  of  P  Ibs., 
the  eccentricity  of  the  load  being  e 
inches. 

For  a  given  cross  section  of  the 
strut  at  a  distance  of  x  inches  from 
the  centre,  the  following  notation  is 
used.  (See  Fig.  135.) 

Total  length  of  strut ...    =  2  /  ins. 

Maximum  thickness  per- 
pendicular to  Neutral 
Axis  =  t  „ 

Moment  of  Inertia  of 
cross  section  about 
N.A.  ...  ...  =  I  in.*  units 

Area  of  cross  section...    =    A  sq.  ins. 

Deflection  under  the 
load  P 


FIG.  135.— Tapered  Strut. 


. . .    =    y  ins. 

For  any  particular  case,  A  and  I 
will  be  functions  of  t. 


The  lateral  load  on  strut    =  w  Ibs.  per  inch  length  of  strut 

. •.  Total  lateral  load  on  strut  =   /  *        ivtdx  Ibs. 

J  x=  -i 

For  the  purposes  of  this  investigation,  w  is  supposed  to  be  a 
function  of  x\  if  all  the  sections  of  the  strut  are  similar,  and  the 
lateral  load  is  due  to  wind  pressure,  then  w  is  constant. 

The  Meridian  Curve  of  the  strut  is  defined  as  the  curve 
whose  ordinates  are  t\  2,  and  whose  abscissae  are  x. 

It  is  now  required  to  find  the  shape  of  this  curve,  so  that 
under  the  influence  of  the  end  load  P,  the  maximum  compres- 
sive  stress  at  every  cross  section  of  the  strut 
=  /lbs.  per  square  inch 


DESIGN    OF   THE   WINGS  175 

The  bending  moment  at  a  cross  section  such  as  A  A 

f  C*   C*  \ 

=  tP(y  +  e-    I       I      wtdx.dx'\ 

o  o 

Maximum  compressive  stress  at  this  cross  section 

rx  rx 
=  ^O7  +  g)  -JoJoWtdx.dx^       P 

-/  (i> 

Omitting  expression  for  lateral  load,  this  becomes 

=  P(-r2V)/+-|=/  (2) 

_    T      /  T»   , 

That  is     y  t  +  e  t  = 

or  v  = 


whence 


The  bending  moment  equation  now  becomes 


that  is       _2 
Let  f  (/)  =  z  and  substitute, 

then  — f  =   -  —<f)(z) 

To  solve  this  differential  equation, 
let  ^_ 


then  *L*  =**  =  **    .d_^_fidJ_ 

dx*      dx      dz       dx~P  dz 


or.  p.dp=   -j(z)dz. 

integrating       \p*  =    -  L  z  dz 


176  AEROPLANE   DESIGN 

To  determine  Cx  we  have  from  Fig.  135  : 

when  x  =  o  :    —  =  o 

d  x 


and  /  =  t,  ;  p  =  "  =  ££   .  ±L 

ax       at       dx 


Also  when  /0  =  /  :   jc  =  o 


/ 
Inserting  value  of  z  from  (3),  we  get 

P 


(4) 


dt  \  t 

Formula  64 


Equation  (4)  will  determine  the  cross  section  t  at  any  dis- 
tance x  from  centre.  If  the  effect  of  the  lateral  load  be  included, 
this  equation  becomes 


/    /"'el     rf     (I/  P   Xl2,/,    ,       /"'»E    OT 

vy  i^i'-TAJr  v  T 


Formula  65  ............    (5) 


DESIGN   OF   THE   WINGS 


177 


Since  at  the  end  of  the  strut  x  =  /,   and  y  =  o  we  have 
from  (i) 


•i    .          /AJ        a/ 

an  equation  which  gives  tr 

Substituting  x  =  I  and  t  —  ^  in  either  (4)  or  (5),  we  have  an 
equation  which  theoretically  determines  tQ 

The  percentage  reduction  of  the  crippling  load  of  a  tapered 
strut  due  to  the  lateral  wind  load  w  is  given  approximately  by 
the  expression 


3    /A, 

4*    P 


if 


>  0-05 


(7) 


A0  representing  the  area  of  the  section  where  the  thickness 


is  /0. 


FIG.  136.  FIG.  137. 

Compression  Rib  Sections. 

Investigations  upon  a  number  of  struts  have  shown  that  this 
correction  is  practically  negligible  except  for  the  wing  struts  of 
high-speed  machines.  For  this  reason  the  term  containing  w 
has  been  neglected  in  the  illustrative  example  showing  the 
practical  application  of  the  above  theory  to  an  actual  strut, 
which  is  set  out  in  full  later  in  this  chapter. 

The  Drag  Struts  and  Bracing. — For  small  machines  the 
general  method  of  taking  the  shear  due  to  the  drag  loads  and 
components  of  the  lift  reactions  is  by  means  of  compression 
ribs.  These  ribs  have  the  correct  contour  of  the  wing  section, 
and  their  web  is  made  solid  in  order  to  resist  the  compression. 
The  section  of  such  a  rib  is  as  shown  in  Fig.  136. 

A  stronger  and  better  method  than  this  is  illustrated  in 
Fig.  137,  in  which  two  ordinary  ribs  with  lattice  webs  are  placed 


i78 


AEROPLANE    DESIGN 


adjoining  one  another.      Such  an  arrangement  is  considerably 
lighter  than  that  shown  in  Fig.  136. 

For  larger  machines  it  becomes  necessary  to  build  hollow 
wooden  struts  of  circular  or  box  section,  or  tubular  steel  struts 
may  be  used.  It  will  generally  be  found  that  the  wooden  con- 
struction will  prove  the  lightest  for  a  given  strength.  Particulars 
of  steel  tubes  which  may  be  used  for  such  purposes  are  given  in 
Appendix. 


Reproduced  by  courtesy  of  '  Flight.* 

FIG.  138. — General  Sketch  of  Internal  Bracing  and  of 
Interplane  Strut  Attachment. 


Their  use  and  mode  of  attachment  is  shown  in  Fig.  138. 

The  Drag  Bracing  wires  usually  take  the  form  of  small 
circular  tie-rods  screwed  at  each  end,  as  shown  in  Fig.  1 30  (c\, 
particulars  of  which  are  given  in  Table  XXVI. 

The  general  arrangement  of  a  drag  strut  and  fitting  is  shown, 
in  Figs.  138  and  139. 


DESIGN   OF   THE   WINGS  179 

Design  of  the  Spars. — The  spars  are  the  most  important 
members  of  the  wing  structure,  and  much  care  must  therefore  be 
exercised  in  their  design  in  order  that  the  necessary  strength 
may  be  obtained  for  the  minimum  possible  weight.  The  larger 
the  machine  and  the  deeper  the  wing  section  employed  the 
more  economically  can  the  spars  be  designed,  but  even  in  this 
case  it  is  not  easy  to  reduce  the  weight  of  the  spars  alone  to  less 
than  one-third  of  the  total  weight  of  the  wing  structure.  In 


FIG.   139. — Internal  Wing  Structure. 

small  machines  the  weight  of  the  spars  may  amount  to  as  much 
as  one-half  of  the  total  weight  of  the  wing  structure.  A  small 
percentage  of  saving  in  the  weight  of  the  spars  will  therefore  be 
relatively  of  much  more  importance  than  a  similar  percentage 
saving  in  any  other  members  of  the  wing  structure. 

Spars  are  subject  to  (a)  Bending  stresses,  (fr)  Direct  end 
loads. 

The  bending  stresses  result  from  the  uniform  distribution  of 


i8o  AEROPLANE    DESIGN 

the  air  forces  along  the  wing  section,  and  the  spars  therefore 
correspond,  as  shown  in  Chapter  IV.,  to  a  continuous  beam 
uniformly  loaded  and  supported  at  various  points  by  means  of 
the  wing  bracing,  and  the  complete  bending  moment  diagrams 
are  drawn  upon  this  assumption  by  the  methods  outlined  in  that 
chapter.  From  the  diagram  so  obtained  the  bending  moment  is 
shown  at  all  points  along  the  span,  and  the  bending  stresses  can 
therefore  be  calculated  from  Formula  51. 

Complete  bending  moment  diagrams  for  the  top  and  bottom 
plane  spars  of  a  small  machine  are  shown  in  Fig.  147. 

Bending  stresses  are  set  up  by  the  lift  forces.,  down  forces, 
and  drag  forces.  The  drag  forces  are  in  the  plane  perpendicular 
to  the  other  two  forces,  but  they  are  usually  so  small  that  they 
can  be  neglected  in  ordinary  practice. 

Direct  end  loads  are  the  horizontal  components  of  the 
tension  in  the  wing  bracing  both  external  and  internal.  A 
reference  to  the  stress  diagrams  for  vertical  frames  shows  that  in 
normal  flight  the  top  plane  spars  are  in  direct  compression  owing 
to  these  end  loads  while  the  lower  plane  spars  are  in  tension. 
In  cases  of  downloading  these  end  loads  are  reversed  in  direc- 
tion. For  the  end  loads  due  to  drag  bracing  it  will  be  seen  that 
with  drag  forces  acting  from  front  to  rear,  the  rear  spars  are  in 
compression  and  the  front  spars  are  in  tension  ;  and  that  these 
directions  are  reversed  when  the  drag  loads  act  from  back  to 
front.  The  actual  loads  are  obtained  from  the  stress  diagrams 
for  the  respective  cases  from  which  the  resultant  stress  at  any 
section  of  the  spar  is  obtained  by  dividing  the  load  by  the  cross- 
sectional  area  at  that  point 

The  total  stress  in  the  spar  at  the  point  considered  is 
therefore 

=  /=  — -  H Formula  66 

I         A 

If  the  spars  are  made  of  silver  spruce,  the  total  stress  obtained 
from  Formula  66  must  not  exceed  4500  Ibs.  per  square  inch  for 
compression,  or  1 1,000  Ibs.  per  square  inch  for  tension. 

CORRECTION  FACTOR  TO  BE  APPLIED  TO  THE  BENDING 
MOMENT  AT  THE  CENTRE  OF  SPANS. — The  effect  of  the  dis- 
tributed load  along  the  spans  will  be  to  produce  a  deflection  at 
the  centre  of  each  bay  relative  to  the  points  of  support  where 
the  external  bracing  is  attached.  As  a  result  the  bending 
moment  at  the  centre  of  the  span  will  be  increased  if  the  end 
load  is  compressive,  and  diminished  if  the  load  is  tensile,  by 
an  amount  which  is  equal  to  the  end  load  multiplied  by  the 
deflection. 


DESIGN    OF   THE   WINGS 


1 81 


In  order  to  allow  for  this  a  correction  factor  is  applied  to 
the  bending  moments  at  the  centre  of  the  spans,  namely  : 


-  P 


Formula  67 


2  7T2  E  I  _  crippling  load  of  spars  considered  as 
where     PE  •*        ji a  strut,  using  Euler's  formula 


and     P 


end  load. 


This  factor  will  be  greater  than  unity  with  compressive  end 
loads  and  less  than  unity  with  tensile  end  loads. 

Some  typical  wooden  spar  sections  are  shown  in  Fig.  140  a, 
b,  c.  From  the  equation  for  bending  stress  (Formula  66)  it  is 
obvious  that  in  order  to  keep  the  stress  low  the  moment  of 
inertia  must  be  large,  therefore  the  material  must  be  concen- 


(a)  (10  te) 

FIG.  140. — Typical  Spar  Sections. 


(50 


trated  as  far  as  possible  from  the  neutral  axis.  This  is  why  an 
'I1  (see  '&'  in  Fig.  140),  or  a  'box'  (see  'c'  in  Fig.  140) 
section  is  preferable  to  the  rectangular  section  shown  at  ' a*  in 
Fig.  140.  It  is  on  this  account  that  the  thin  wing  possesses 
unduly  heavy  spans,  and  of  course  where  the  depth  is  small  the 
rear  span  is  very  difficult  to  design.  The  spar  shown  at  * '  d*  in 
Fig.  140  is  made  of  No.  22  S.W.G.  sheet  steel,  being  built  up  of 
two  corrugated  channel  sections  to  form  the  web,  and  riveted 
to  two  corrugated  flange  plates  at  either  end.  Such  a  spar  can 
be  made  very  light,  is  easy  to  manufacture,  and  it  is  very  pro- 
bable that  the  near  future  will  see  a  large  development  of  steel 
spars  built  up  in  this  manner. 

A  very  interesting  type  of  spar  section  and  internal  wing 
arrangement  is  that  adopted  on  the  Fokker  wireless  triplane, 
which  is  illustrated  in  Fig.  141.  As  will  be  seen  from  this 
figure,  the  two  spars  (each  of  the  box  type)  are  placed  very 
close  together,  and  then  the  two  box  sections  are  united  by  a 
sheet  of  three-ply  covering.  As  a  result  of  this  uncommon 
arrangement  all  internal  wing  bracing  has  been  avoided. 


182 


AEROPLANE  DESIGN 


O 


O 
t) 

O 


O, 


DESIGN   OF   THE   WINGS  183 

Practical    Example    of  Wing   Structure    Design.— The 

preceding  work  upon  the  detailed  design  of  the  wing  structure 
members  will  now  be  applied  to  the  machine  for  which  the 
preliminary  stress  diagrams  have  already  been  drawn  and  shown 
in  Figs.  125  and  126. 

The  wing  section  chosen  for  this  machine  is  the  R.A.F.  6, 
shown  in  Fig.  40. 

NORMAL  FLIGHT. — The  travel  of  the  C.P.  is  from  -3  to  -55 
of  the  chord — that  is,  for  a  six-foot  chord  from  21*6"  to  39'6" 
from  the  leading  edge. 


FIG.  142. 

Spacing  the  spars  as  shown  in  Fig.  142, 
The  maximum  proportion  of  the  load  on  front  spar 

=  39'°  -  *2'6  =  68% 

39 
and  the  maximum  proportion  of  load  on  rear  spar 


A  factor  of  safety  of  7  will  be  used  throughout,  and  the 
method  of  duplication  employed  will  be  direct. 

The  factor  due  to  stagger  =  --  -  =  —    -  =  i  '053 

Hence  the  maximum  load  in  the  front  frame  members 

=  load  in  vertical  frame  from  stress  diagram   x  7  x  -68  x  ro53 

=  5  x  stress  diagram  load 
and  the  maximum  load  in  the  rear  frame  members 

=  stress  diagram  load  x   7   x    '79  x   1*053 

=  5*82   x  stress  diagram  load. 

DOWNLOADING.  —  The  position  of  the  centre  of  pressure  for 
downloading  may  be  taken  at  '25  chord,  or  at  18"  from  the 
leading  edge. 

The  maximum  proportion  of  downloading  on  front  frame 

=  39-9  =  77=/ 

39 
whence  proportion  for  the  rear  frame  =  23% 


184  AEROPLANE    DESIGN 

The  maximum  load  on  the  front  frame  downbracing 

=  downloading  stress  diagram  load  x  L  x  -77  x  1*053 

=  2*84  x  downloading  stress  diagram  load 
and  maximum  load  on  rear  frame  downbracing 

=  downloading  stress  diagram  load  x  3-5  x  -23  x  1*053 

=  0-85  x  downloading  stress  diagram  load. 

Proceeding  to  detail  design    and   inserting   two  wires  each 
capable  of  taking  two-thirds  of  the  maximum  load,  we  have 

EXTERNAL  BRACING. 


Stress 

FRONT 

FRAME. 

REAR 

FRAME. 

Load. 

Maximum 
Load. 

Size  of  Wire. 

Maximum 
Load. 

Size  of  Wire. 

Factor  5*0 

Factor  5-82 

Lift  wire  B  c1 

440 

2200 

2 

-  2  B.A. 

2560 

2 

-   2  B.A. 

Lift  wire  c  D1 

950 

4750 

2 

-  i"B.S.F. 

5520 

2 

Factor  2*84 

Factor  '85 

Down  wire  c  B1 

435 

1235 

2 

-  4  B.A. 

370 

2 

-  4  B.A. 

Down  wire  D  c1 

940 

2670 

2 

-  2  B.A. 

800 

2 

-  4  B.A. 

I 

DESIGN  OF  THE  INTERPLANE  STRUTS.— The  load  on  the 
interplane  struts  for  various  flight  conditions  follows  directly 
from  the  stress  diagrams. 

INTERPLANE  STRUTS. 


Strut. 

Load  from  Stress  Diagram. 

Maximum  Loads. 

Front  Frame. 

Rear  Frame. 

AB1 

Lift  forces 
Down  forces 

+    80  Ibs. 
80   „ 

+    400  Ibs. 

227    „ 

+    465  Ibs. 
68    „ 

BB1 

Lift  forces 
Down  forces 

-  142    ., 
-  i55    » 

7TQ    „ 

440  „ 

827  „ 

-        132    **, 

CC1 

Lift  forces 
Down  forces 

-  472    » 
-  49°    »» 

-  2360  „ 
-  1390  ,, 

-  2750  „ 
417  ,» 

D  D1 

Lift  forces 
Down  forces 

+  "5   >» 
-  790    » 

+    575    >i 
-  2240    „ 

670  „ 
670  „ 

DESIGN   OF   THE   WINGS  185 

The  loads  for  which  it  is  necessary  to  design  each  strut  are 
underlined.  With  regard  to  the  strut  A  B1,  it  is  necessary  to 
design  this  for  the  downloading  forces  because  this  strut  is 
certain  to  fail  under  compression  and  not  under  tension. 

In  order  that  the  theory  of  the  tapered  strut  already  out- 
lined in  this  chapter  may  be  fully  appreciated,  and  the  com- 
plicated results  obtained  made  available  for  general  design 
of  struts,  its  use  will  be  illustrated  in  the  design  of  the 
strut  CC1. 

Design  of  the  Interplane  Strut  C  C1,  according  to  the  tapered 
strut  formulae  given  on  pages  174-176  :  — 

Length  of  strut  ......         6ft.  4  ins. 

Maximum  compression  ...         2800  Ibs 

Fineness  ratio  .........         3*5  :  i 

Form  of  cross  section  as  shown  in  Fig.  91. 
Area  of  cross  section  ...         ...         2  '5  f2 

Least  moment  of  inertia         ...         =  0*15  /4 
Taper  to  be  from  a  maximum  at  the  centre  cross  section 
down  to  the  points  of  support. 

In  order  to  find  /0  and  the  correct  taper  of  the  strut,  it  is 
necessary  to  apply  the  theory  shown  on  pages  174-176.  At 
first  sight  this  would  appear  to  be  a  difficult  process,  but  by 
taking  each  equation  separately,  and  dealing  with  these  portions 
in  the  manner  indicated,  the  solution  of  the  whole  equation  can 
be  obtained  without  any  knowledge  of  advanced  mathematics, 
although,  as  will  be  seen,  the  process  is  somewhat  lengthy. 

Consider  first  the  expression 


.,       - 

Jt\*\l  /A 

This   expression    represents   the  rate  of  change   of  the  slope 
of  the  function 


with  respect  to  /.  In  order  to  obtain  this  rate  of  change  it  is. 
therefore  necessary  to  draw  the  curve  of  this  function,  and 
measure  its  slope  at  various  values  of  /.  Alternatively,  but  by 
taking  much  smaller  intervals,  the  value  of  this  slope  could  be 
obtained  by  tabular  integration  in  the  manner  shown  for 
bending  moments  and  deflections  in  Chapter  IV.  The  work 


186  AEROPLANE    DESIGN 

preparatory  to  graphing  the  function  should  be  set  out  in  the 
following  manner : 


1-25 

r5 

1*75 

2*0 

1-56 

2-25 

3*06 

4*0 

2-44 

5-06 

9-40 

16*0 

3-92 

5-63 

7-65 

I0'0 

0-366 

0*76 

1-41 

2-4 

0-293 

0-506 

0*805 

1*2 

A  =  2*5  t*  2*5 

I  =  0-15  /4  0-15 

I 

7  °'r5 

P          2800 

/A  =  CCQO  A  °'204       0*13         0*0905       0-0665       0*051 


p 

i  -  j^        0-796   0-87    0-9095   0-9335   °'949 

I   /  P  , 

0-1193     °'255       0*46  0-751 


The  curve  for  this  function  can  now  be  plotted  from  these 
figures.  The  next  step  is  to  draw  the  tangents  to  the  curve  for 
the  values  of  /  taken.  These  tangents  give  the  slope  of  the  curve 
at  these  points,  that  is,  they  give  the  value  of  the  expression 


dt{t\       /A 

as  below  : 


i  1-25         1-5  1*75         2-0 

~  7T  )  h     °'44          0-72          0-94          1-35          1*82 


and  from  these  values  the  graph  of  the  expression  can  be  drawn. 
(See  Fig.  143.) 

The  denominator  of  the  equation 


A/  A>  if  d 

vy  lU 


P 


must  next  be  considered,  and  examination  of  this  expression 
shows  that  it  is  required  to  find  the  square  root  of  the  area  of 
the  curve  represented  by  the  expression 

i      d  fl 


DESIGN   OF   THE   WINGS 


187 


between  the  values  of  /  and  /0.  The  value  of  /0  is  being  sought, 
so  that  two  or  three  other  values  of  t  must  now  be  chosen  and 
used  to  arrive  at  the  value  /0  required.  The  method  of  pro- 
cedure will  be  clear  as  the  example  progresses.  Referring  to 
the  above  expression  it  is  seen  that  it  represents  the  rate  of 
change  of  slope  of  the  square  of  the  expression  whose  value  has 
just  been  found  multiplied  by  I/I. 


FIG.  143. 


It  is  therefore  necessary  to  square  the  various  values  ob- 
tained for 

K-  -A) 

and  then  to  draw  the  curve  for  the  results  obtained,  draw  the 
tangents  for  the  values  of  /  under  consideration,  and  then  to 
measure  the  slopes  of  the  tangents  obtained  as  in  the  work 
dealing  with  the  numerator.  The  values  so  obtained  are  then 
multiplied  by  i/I,  and  from  the  results  the  graph  of  the 
complete  expression  can  be  drawn.  The  tabular  arrangement 


1  88  AEROPLANE    DESIGN 

of  the  work  is  shown  below,  and  the  various  curves  are  shown  in 
143- 

/  i  1-25       1-5         175       2-0 

0<I425    0-65          0-212       0-564       I-3 


--}} 

/A/J 


0-12  0-36  0^2  I-96 


i       d    (  I  /  p  V|2 

I  'Jf\7  V  ~fAjf  ro°       I>21        r39        1-63 

For  the  remainder  of  this  chapter  we  shall  replace   these 
complicated  expressions  by  the  following  symbols  :  _ 


Expression. 

Symbol. 

P 

K 

/A 

7(1-  yjr] 

L 

t   \        /A/ 

d  f  i  /       p  \| 

M 

<//  i/   V        /A/J  

{?(I'"7s)}8=L8=      - 

...     N 

dt  \1  V1  ~/A)/  =77  = 

...      P 

i      d    (\  f          P  \1  2 

I  '  Tt  \1  v  "/Ay/ 

...      Q 

rt(t  j      d    (I   f          P  \12 

7  I-^UO-TA)}"    

...      R 

.  I          d      I  I     /  P 

i •  r/ {/- 11 -/A 


The  values  of  Q  are  plotted  against  t  as  shown  in  Fig. 
143.  The  area  of  this  curve  between  /0  and  various  values 
of  /  will  give  the  value  R.  Selecting  three  values  of  /0  and 
measuring  the  areas  under  the  curve  between  the  ordinates  tQ 
and  each  value  of  t  considered,  taking  the  square  root  of  each  of 
these  areas,  and  then  dividing  each  value  so  obtained  into  the 


DESIGN    OF   THE   WINGS  189 

corresponding  value  of  M  already  determined,  we  arrive  at  the 
ordinates  of  the  final  curves.  For  this  investigation  the  values 
2*0",  175",  and  1*5"  for  /0  have  been  selected.  The  tabular 
arrangement  of  the  work  is  shown  below,  and  it  must  be  borne 
in  mind  in  calculating  these  areas  that  the  scales  to  which  the 
graphs  have  been  drawn  are  of  prime  importance. 

/0  -  2-0" 


/ 

I'O 

I 

•25 

I- 

5 

I 

75 

i  '95 

i'975 

i'975 

R 

1-194 

0 

•971 

0* 

70 

0 

•378 

0-08 

0*0405 

0-0203 

S 

1*092 

0 

•985 

O* 

836 

0 

"614 

0-283 

0"O20I 

0*0142 

M 

0-44 

0 

•69 

0 

•970 

I 

"34 

1-71 

1-77 

1'795 

M 
S 

0-403 

0 

•70 

I' 

16 

2 

•18 

6*05 

8-8 

I2'6 

/ 

I'O 

1*25 

i  -5 

1-70 

1-725 

!-7375 

R 

0*818 

°'595 

0-322 

0*0685 

0-0345 

0*0173 

S 

0^904 

0*771 

0*568 

0^262 

0*186 

0-1315 

M 

0*44 

0*69 

0*97 

1-255 

1*30 

1*32 

M 

S 

0*49 

0*895 

1*71 

4*80 

7*00 

10*00 

'o 

•  1*5 

/ 

I'O 

1*25 

r45 

i-475 

I-4875 

R 

0*495 

0*272 

0*058 

0*0294 

0*0147 

S 

0*704. 

0*522 

0*242 

0*1715 

0*121 

M 

0*44 

0*69 

0*91 

0*94 

0-95 

M 

S 

0*625 

1*32 

376 

5'49 

7^5 

The  areas  of  the  curves  obtained  by  plotting  these  values 
against  tQ  enable  a  value  of  /0  satisfying  the  equation  to  be 
determined.  The  integral  or  area  curves  are  shown  in  full  lines, 
and  those  representing  the  complete  function  in  chain  lines.  (See 
Fig.  144.)  The  maximum  ordinates  of  the  integral  curves  will  be 
found  to  lie  on  a  straight  line,  hence  by  joining  up  these  points  a 
straight  line  is  obtained  which  represents  the  value  of  the  integral 


M.dt 


for  all  values  of  t0 


190  AEROPLANE   DESIGN 

The  particular  value  of  the  integral  required  is  determined 
by  putting  x  —  I  =  J  total  length  in  the  left-hand  side  of  the 
equation  5. 

Then  area  required      =  76       /     2800 

2      *    i '6  x  io6 
=  1*59  square  inches. 

From  the  curve  the  value  of  /0  which  gives  this  area  is 
1*83",  therefore  the  maximum  thickness  of  the  strut  is  1*83"  and 
its  length  =  1*83  x  3-5  =  6-4" 

SHAPE  OF  THE  STRUT.— The  value  of  /0  thus  found  is  now 
substituted  in  the  general  expression,  and  curve  4  integrated 
back  from  this  point.  The  value  of 

f83 
Q.dt 

r 

t 

is  determined  for  various  values    of  /  and  the   corresponding 
values  of  x  obtained. 

Arranged  tabularly  we  have  : 

/     1*8125     1*80        1*75       1*625     1*5         1*25         1*0 
0*0182     0*0363    o  107     0*274     0*428     0*700       0*922 


f^Q.Jt 
M 

o'i35 
i'45 

0*I9I 

IH25 

0-327 
i*34 

0*524 
1*14 

0*654 

0*97 

0*837 
0*685 

0*960 
o*45 

M 

S 

10*75 

7'45 

4*i 

2*20 

1-48 

0-82 

0*469 

f12   M.dt 

1*80 
0*26 

6-23- 

J'75 

o*54 
12*9" 

1-70 
0*71 
17" 

1*60 
0*96 

23" 

i  '5 
1-14 
27'3" 

1*25 
1*42 
34" 

1*0 

1*58 
37'8" 

(         s 

x 

>  =  3-5  ' 

6-3" 

6*125 

"     5*95" 

5'6" 

5*25" 

4*375" 

3*5" 

*J 

N.B.     x  - 

1*2 

K( 

K1-. 

/A)/] 

\dt 

it 

r'i[ 

M\( 

'-A 

)F> 

DESIGN   OF   THE   WINGS 


191 


The  shape  of  the  strut  can  then  be  drawn  out  from  the  values 
obtained  above  for  x  and  /,  as  illustrated  in  Fig.  145. 

DESIGN    OF   THE    DRAG    BRACING.  —  In   accordance   with 
standard  general  practice  the  total  drag  force  to  be  distributed 


FIG.  144. — Graphical  Evaluation  of  Tapered  Strut  Formula. 


over  the  planes  will  be  taken  as  one-seventh  of  the  weight  of 
the  machine.     Hence  drag  force 


2000 


=  286  Ibs. 


=  072  Ibs.  per  square  foot. 

This  load  is  assumed  equally  carried  by  the  front  and  rear 
spar.  The  plan  of  the  wings  must  next  be  drawn  out  and  the 
spacing  of  the  drag  struts  decided  upon.  A  suitable  arrange- 


192  AEROPLANE    DESIGN 

ment  is  shown  in  Fig.  146.     The  forces  at  the  joints  due  to  the 
drag  forces  is  then  determined  in  the  following  manner  :  — 

Area  of  outer  section  of  top  plane  from  joint  A  to  tip 

=  14  sq.  feet  approx. 
Drag  load  on  this  area 

=  14  x  0*72  =  10  Ibs. 

This  is  equally  distributed  between  the  front  and  rear  joints 
of  A  and  A1 

Area  of  wing  between  A  and  B 

=  4  x  6  =  24  sq.  feet.  .  * 

Drag  load  over  this  area 

=  24  x  0*72  =  17  Ibs.  approx. 

Half  of  this  acts  at  A  and  A1,  and  the  other  half  at  B  and  B1. 
Proceeding  along  the  span  in  this  manner  the  drag  forces  at 
each  of  the  joints  are  obtained,  and  the  results  should  be 
tabulated  as  under  :  — 

TOP  PLANE. 

a  b       -      c         '    d  e  f  g 

Area  of  drag  bay         ...     14         24         21         18         18         18         15 
Drag  load  —  Ibs.          ...     10         17         15         13         13         13         n 

f  Front  o'o        8'o        7%*o        6x        6's        6'o 

Reactions 

I  Rear  9-0        8'o        7*0        6-5        6-5        6'o 

BOTTOM  PLANE. 

j  k  I  m  n 

Area  of  drag  bay         ...  14         20         18         18         18 

Drag  load  —  Ibs.          ...  10         15         13         13         13 

•n        •  f  Front  8-5        7-0        6x        6-15        3-0 

Reactions       ...{*»  * 

I  Rear  8-5        7-0        6-5        6-5        3-0 

In  addition  to  these  loads  there  will  be  horizontal  com- 
ponents due  to  the  inclination  of  the  lift  bracing  owing  to  the 
stagger  arrangement.  These  are  obtained  by  multiplying  the 
lift  reactions  at  each  point  of  support  by  the  factor 


stagger       6       3 

The  components  thus  obtained  are  added  to  the  reactions 
due  to  the  drag  forces  and  the  drag  bracing  stressed  in  the 


DESIGN   OF   THE   WINGS 


193 


usual    manner.      In    adding    the    lift    components    it    is    first 
necessary    to    apply    both    the    C.  P.    and    safety    factors    to 


Curve  2.      Jnfeyal  Curve   of  ( 


Meridian  Curve  Of  Strut-     


ti— 





S«fe  V,CM    Of      Si-rut 

FIG.  145. 

the  original  reactions.     The  coefficients    to  be  applied  are  as 
^follows : — 

(a)  Centre  of  pressure  forward  : 

Front  frame  =  7  x  '68  x  "33  =  1-59 
Rear  frame    =7  x  '32  x  "33  =  0*75 

(b)  Centre  of  pressure  backward : 

Front  frame  =  7  x  '21  x  -33  =  0*49 
Rear  frame    =  7  x  -79  x  -33  =  1*84 


194  AEROPLANE    DESIGN 

These   coefficients   applied   to   the    lift    reactions  give   the 

following  horizontal  loads  which  must  be  taken  by  the  drag 
bracing : — 

TOP  PLANE. 

Joint A            B             c  D 

Lift  reaction  on  vertical  frame         64  155         202  115 

(a)  C.P.  forward,  hori-)  Front       102  246         321  183 
zontal  components/   Rear         48  116         151  86 

(b)  C.P.    back,    hori- \Front         31           76           99  56 
zontal  components/  Rear       118  286         372  212 

BOTTOM  PLANE. 

Joint B'  c'  D' 

Lift  reactions  on  vertical  frame         78  176  62 

(a)  C.P.  forward,  hori-^  Front  124  280  98 

zontal  componentsj    Rear         58  132  46 

(£)   C.P.    back,   hori-|  Front         38           86  30 

zontal  components/  Rear  144  324  114 

STRESS  DIAGRAMS  FOR  DRAG  BRACING.— The  reactions 
thus  obtained  are  added  to  the  local  drag  reactions,  and  the 
stress  diagrams  for  the  drag  bracing  can  then  be  drawn  as 
shown  in  Fig.  146.  It  will  be  observed  that  in  the  case  of 
normal  flight  the  drag  bracing  wires  shown  in  full  lines  will 
alone  be  in  operation,  whereas  in  the  case  of  downloading  the 
dotted  bracing  will  be  in  action.  It  is  customary  to  make  the 
two  bracing  wires  in  each  bay  similar,  so  that  it  is  not  necessary 
to  make  a  stress  diagram  for  the  drag  bracing  under  down- 
loading forces. 

Further  examination  shows  that  it  is  only  necessary  to  stress 
the  drag  bracing  for  the  lift  conditions  with  the  centre  of 
pressure  forward.  The  stress  diagrams  therefore  reduce  to  one 
for  each  plane.  The  factor  having  been  applied  to  the  reactions 
before  drawing  the  diagrams,  the  individual  stresses  in  the 
members  can  be  read  directly  from  the  diagram  and  tabulated 
for  reference  as  shown. 

DESIGN  OF  THE  DRAG  BRACING. — Circular  tie-rods,  of 
which  particulars  have  already  been  given  in  Table  XXVI.  and 
illustrations  in  Fig.  1 30  (c\  may  be  used.  From  the  table  the 
sizes  necessary  are  : 

TOP  PLANE. 

Bracing  wire     ...     14-15       16-17       18-19       20-21         22-23 
Load — Ibs.        ...      +  280       +  800       +770       +  1450       +  1470 
Tie-rod  size  4  B.A.      4  B.A.      4  B. A.      2  B. A.        2  B. A. 


DESIGN   OF   THE   WINGS  195 

LOWER  PLANE. 
No.  4  B.A.  tie-rods  throughout. 

DESIGN  OF  THE  DRAG  STRUTS. — For  such  a  small  machine 
as  that  under  consideration  it  would  be  preferable  in  practice  to 
insert  compression  ribs,  but  for  purposes  of  further  illustration 
we  will  assume  that  steel  tubes  of  thin  gauge  are  to  be  used  as 
compression  members.  The  size  of  tubes  necessary  will  there- 
fore be  determined  by  use  of  Formula  62  (Rankine's  Formula), 
where  the  constants  have  the  following  values : — 

fc  =  2 1  tons  per  square  inch. 

a   =  1/7500 

L  =  length  =  39" 

TOP  PLANE  STRUTS. 

Drag  Strut  ...  1-14  15-16  17-18  19-20  21-22  23-24 
Load — Ibs.  ...  -no  -430  -560  -890  -1050  -1250 
Diameter  of  tube, 

22S.W.G.    ...        J"       f"       r        F         F 

BOTTOM  PLANE  STRUTS. 

Drag  Strut  ...  6-n  12-13  14-15  16-17 
Load — Ibs.  ...  -130  -220  -490  -660 
Diameter  of  tube, 

22S.W.G.     ...  i"          4"  I"  f" 

DESIGN  OF  THE  SPARS. — The  stresses  in  the  spars  are  due 
to  bending  and  direct  end  loads.  In  order  to  determine  the 
bending  stresses  it  is  necessary  to  draw  the  complete  bending 
moment  diagrams  for  the  top  and  bottom  planes.  The  fixing 
moments  at  the  supports  have  already  been  obtained.  In  order 
to  complete  the  diagrams,  the  free  bending  moment  diagrams 
are  drawn  upon  each  span  for  uniform  loading.  As  shown  in 
Chapter  IV.,  these  free  B.M.  diagrams  will  be  parabolas  with 
their  maximum  ordinates  equal  to  w  /2/8 

Hence  in  the  case  under  consideration  the  maximum  B.M. 
ordinates  are  : — 

TOP  PLANE. 

Span  ...          ...          ...          ...       ab          be  cd  de 

Maximum  B.M. — Ibs.  ft       ...       50         158         135         23-4 

LOWER  PLANE. 
Span  ...          ...          ...          ...        b' c         c  d' 

Maximum  B.M. — Ibs.  ft.     ...       135         115 


i96 


AEROPLANE   DESIGN 


The  parabolas  and  the  fixing  moments  are  set  out  to  the 
same  scale,  and  the  net  bending  moment  diagrams  are  shown 
shaded  in  Fig.  147,  from  which  figures  the  value  of  the  bending 
moment  at  any  point  along  the  span  can  be  read  off  directly. 


f    57lbs  \ZA 

I    A.J       ®     ai 


Lmear  Scale 


Ffeacrions  due   to  Stagger 


Joint- 

A 

B 

c 

D 

Front*  FcAme 

wa 

£46 

321 

185 

Rw>r    . 

>»8 

116 

151 

at 

Re-vchons  due    to   Stagge 


Joiaf 

B' 

C' 

D' 

Front'  Fc4mc 

124^ 

280 

as 

Rea-r      . 

58 

isa 

46 

FIG.  146. — Stress  Diagrams  for  Drag  Bracing. 

To  the  values  thus  obtained  the  requisite  factor  of  safety  and  the 
centre  of  pressure  coefficients  for  the  front  and  rear  spars  must 
be  applied. 

LIFT  FORCE  FACTORS. 
Factor  for  front  spar  =  7  x  -68  =  4-76 
Factor  for  rear  spar    =  7  x  79  =  5*53 


DESIGN   OF   THE  WINGS  197 

Tabulating  the  bending  moments  for  various  positions  along 
the  spans,  we  have  the  following  tables  : 

TOP  PLANE. 

B.M.  Maximum  B.M. 

Position.  on  diagram.  Front  spar.  Rear  spar. 

Ibs.  ft.  Ibs.  ft.  Ibs.  ft. 

Joint  A 25  ...  119  ...  138 

Middle  of  span  A  B     ...  negligible  ... 

Joint  B     77  ...  366  ...  426 

Middle  of  span  B  c     ...  65  ...  310  ...  359 

Joint  c     ...  114  543  •-•  63° 

Middle  of  span  c  D     ...  50  ...  238  ...  276 

Joint  D 54  257  298 

Middle  of  span  D  E     ...  30  ...  143  ...  166 

LOWER  PLANE. 

Joint  B' 16  ...  76  ...  88 

Middle  of  span  B' c'    ...  75  ...  357  ...  415 

Joint  c' 105  ...  500  ...  580 

Middle  of  span  C'D'   ...  45  ...  214  ...  249 

Joint  D' 38  ...  181  ...  210 

Middle  of  span  D' E'   ...  38  ...  181  ...  210 

DOWNLOADING. — The  bending  moments  on  the  spars  due  to 
downloading  forces  follow  in  the  same  manner  by  applying  the 
correct  factors  for  the  centre  of  pressure  and  safety.  In  general 
it  is  necessary  to  consider  the  lower  spars  only  for  downloading 
forces,  as  they  will  then  be  in  compression,  whereas  in  normal 
flight  they  are  in  tension.  The  much  greater  strength  of  spruce 
in  tension  as  compared  with  compression,  may  result  in  the 
necessity  of  designing  the  lower  spars  for  downloading  forces  in 
spite  of  the  reduced  factor  of  safety  employed. 

DOWNLOADING  FORCE  FACTORS. — LOWER  PLANE  SPARS. 

Factor  for  front  spar  =  3-5x77  =  2-69 
Factor  for  rear  spar    =  3-5  x  '23  =  '805 

B.M.  Maximum  B.M. 

Position.                     on  diagram.  Front  spar.  Rear  spar. 

Ibs.  ft.  Ibs.  ft.  Ibs.  fif. 

Joint  B' 16  ...  43  ...  13 

Middle  of  span  B' c'    ...         75  ...  202  ...  60 

Joint  c' 105  ...  283  ...  85        j- 

Middle  of  span  c' D'   ...         45  ...  121  ...  36 

Joint  D' *    ...         38  ...  102  ...  31 

Middle  of  span  D' E'  ...         38  ...  102  ...  31 


i98 


AEROPLANE    DESIGN 


The  correction  factor  for  end  loads 

P, 


Formula  67. 


PE  -  P 

has  not  been  applied  to  the  bending  moments  at  the  centre  of 
the  spans  in  this  example.  This  correction  should  not  be 
omitted  in  actual  practice. 


Bending-    Moment    Diagrams    -   Load  Factor  <=  I 


4D 


Scales  :- 
Linear 
Bending  Monwnt- 


"TopPUne  Spars 


IB'  |c' 

Bottom    Ranc  Spars 


She»r    Force   Diagrams         load  factor  =   I    


Force  Scale  ••— 


_ 
?OQ         zoo  Ibs. 


lop   Plane    Spans 


FIG.  147. — Design  of  the  Wing  Spars  B.M.  and  S.F.  Diagrams. 

The  bending  moments  along  the  spars  having  been  de- 
termined, the  next  step  is  to  deduce  the  direct  end  loads  upon 
the  spars  resulting  from  the  tension  in  the  lift  and  drag  bracing. 
These  are  read  off  from  the  stress  diagrams.  In  the  case  of  the 
loads  obtained  from  the  lift  and  downloading  stress  diagrams, 
factors  must  be  applied  as  in  the  preceding  work.  The  loads 


DESIGN   OF   THE   WINGS  199 

due  to  drag  forces  are  read  off  directly.  It  will  be  observed  that 
from  the  drag  bracing  stress  diagram  for  the  top  plane,  shown  in 
Fig.  146,  the  front  spar  is  in  tension  and  the  rear  spar  in  com- 
pression. The  result  of  this  is  that  the  drag  forces  on  the  front 
spar  tend  to  reduce  the  direct  load  in  the  front  spar,  since  the 
top  plane  spars  are  in  compression  due  to  the  lift  bracing,  while 
they  increase  the  direct  load  on  the  rear  spar. 

DIRECT  END  LOADS  ON  THE  SPARS. 
(Top  Plane — Compression  due  to  lift  bracing.) 

Span AB  BC  CD  DE 

Front  spar    214         1760         4950         495°  Ibs. 

Rear  spar      249         2040         5750         5750  Ibs. 

LOADS  DUE  TO  DRAG  BRACING. 

Span b               c               d               e               f  g 

Front  spar          o            +220        +820      +1360     +2360  +3360  Ibs. 

Rear  spar...    -220        -820      -1360      -2360      -3360  -  3360  Ibs. 

RESULTANT  END  LOADS  ON  TOP  PLANE  SPARS. 
Front  spar — 

Lift       ...     -214      -1760      -1760      -4950      -4950      -4950  Ibs. 
Drag    ...    +     o      +    220      +    820      +1360      +2360      +3360  Ibs, 


Total    ...  -214  -1540  -    940  -3590  -2590  -  1590  Ibs. 

Rear  spar — 

Lift       ...  -249  -2040  -2040  -5750  -5750  -5750  Ibs. 

Drag     ...  -220  -    820  -1360  -2360  -3360  -  3360  Ibs. 


Total    ...     -469      -2860      -3400      -8110      -9110      -91 10  Ibs. 

In  a  similar  manner  the  direct  loads  upon  the  lower  plane 
spars  under  normal  flight  conditions  can  be  calculated.  With 
downloading  forces  the  same  procedure  is  adopted,  the  end 
loads  being  read  off  the  respective  stress  diagrams  for  the 
external  and  drag  bracing  under  these  conditions.  The  work 
should  be  set  out  in  exactly  the  same  manner  as  shown  above 
for  the  top  plane  spars. 

DESIGN  OF  THE  SPARS.— The  tables  of  direct  loads  in  the 
spars  indicate  that  the  top  rear  spar  will  be  the  most  heavily 
loaded,  and  therefore  it  is  selected  in  order  to  illustrate  the 


200  AEROPLANE   DESIGN 

method  to  be  adopted  in  the  general  design  of  a  spar.  The 
following  figures  relating  to  this  spar  have  been  obtained  :  — 

Span    ......         b  c  d  e  f  g 

Maximum  B.M.  426  426  630  630  298  298  Ibs.  ft. 
Direct  end  load  -469  -2860  -3400  -8110  -9110  -9110  Ibs. 

It  is  necessary  to  select  spar  sections  capable  of  carrying 
these  loads  safely.  The  depth  of  the  spar  is  already  fixed  by 
the  aerofoil  section  chosen.  This  in  the  present  case  is  the 
R.A.F.  6  with  a  6  ft.  chord,  and  with  the  spars  in  the  position 
shown  in  Fig.  142  the  depth  for  the  front  and  rear  spars  is 
limited  to  about  y$".  This  depth  will  therefore  be  taken,  the 
spars  will  be  made  of  I  section,  and  will  be  lightened  out 
towards  the  wing  tips  by  diminishing  the  depth  of  the  flange. 
The  dimensions  of  the  spar  at  various  points  along  the  span  can 
now  be  determined,  and  a  suitable  series  of  sections  are  indicated 
in  Fig.  148. 

Considering  the  section  for  bay  e, 

9  M.I.  =  —  (2  x  3'53  -  1-5  x  23) 

=  6"  14  inch4  units 
A.  -  7  -  3 

=  4  inch'2  units 

Bending  stress  =  J3°  x  I2  x  r?5 

' 


=  2155  Ibs.  per  square  inch. 

Direct  stress     =  -5ll° 

4 

=  2027  ibs.  per  square  inch. 
Total  stress       —  4182  Ibs.  per  square  inch. 

The  maximum  compressive  stress  being  4500  Ibs.  per  square 
inch  for  a  spruce  spar,  this  section  is  evidently  satisfactory. 
Considering  the  section  for  bays/*,  g^  d, 

M.I.  =  5*2  inch4  units 
A.      =3*25  inch2  units 

Maximum  bending  stress  in  bays/and  £  =  1205  Ibs.  per  sq.  in. 
Maximum  =  direct  stress  in  bays  f  and  g  =  2805  Ibs.  per  sq.  in. 

Total  stress  =  4010  Ibs.  per  sq.  in. 

Maximum  bending  stress  in  bay  d  =  2540  Ibs.  per  sq.  in. 

Maximum  direct  stress  in  bay  d      =  1045  Ibs.  per  sq.  in. 

Total  stress  =  3585  Ibs.  per  sq.  in. 

This  section  is  therefore  suitable  for  these  bays. 


DESIGN    OF   THE   WINGS 


201 


Considering  the  section  for  bays  a,  by  c, 

M.I.  =  4*55  inch4  units 
A.      =  2*87  inch2  units 

Maximum  bending  stress  =  1965  Ibs.  per  sq.  in. 

Maximum  direct  stress      =    997  Ibs.  per  sq.  in. 

Total  stress  =  2962  Ibs.  per  sq.  in. 

As  will  be  seen,  this  section  is  very  much  stronger  than  re- 
quired ;  but  as  it  is  not  practicable  to  make  the  thickness  of  the 
flanges  less  than  that  indicated  in  the  figure,  this  section  should 
be  used  over  the  outer  portion  of  the  wing.  Finally,  the  strength 


Seofton     far    Baya  die 


Sccfton    for    Bays 


Bay    e 


Tob     Rear      Spar 


FIG.  148. — Design  of  Wing  Spar. 


of  the  spar  in  shear  should  be  investigated.  On  referring  to 
the  shear  force  diagram  shown  in  Fig.  147  it  will  be  seen  that 
the  maximum  shear  occurs  at  the  joint  C,  at  which  point  the 
shear  is  equal  to 

202  x  79  x  7  =  1 1 20  Ibs. 

whence  the  shear  stress  approximately 


1120 

3*5  x  2 


=  1 60  Ibs.  per  sq.  inch 


since  the  section  is  rectangular  at  the  joint  in  order  to  accom- 
modate the  fitting.  A  shear  stress  of  800  Ibs.  per  square  inch  is 
permissible  across  the  grain  of  spruce,  so  that  the  sections  are 
quite  safe  as  regards  shear. 


202  AEROPLANE    DESIGN 

This  completes  the  design  of  this  spar,  and  by  following  a 
similar  procedure  in  the  case  of  the  remaining  spars  the  requisite 
sections  can  be  determined  and  the  spar  detail  drawings  pre- 
pared. 

Having  settled  the  spar  sizes,  the  design  of  the  members  of 
the  wing  structure  is  finished  and  a  close  estimate  of  the  total 
probable  weight  when  manufactured  can  be  obtained.  This 
should  be  compared  with  the  weight  assumed  for  the  initial 
stressing  of  the  wings,  with  which  it  should  agree  fairly  closely. 

Before  leaving  the  question  of  wing-stressing,  an  example 
will  be  given  of  the  alteration  in  the  stresses  when  the  method 
of  duplication  through  the  incidence  bracing  is  adopted.  It  is 
supposed  that  the  front  lift  wire  c  D'  (Fig.  127)  is  broken,  and 
that  the  load  originally  carried  by  this  wire  is  now  transmitted 
by  the  incidence  wire  c  c'  to  the  rear  frame.  What  will  be 
the  effect  of  this  upon  the  stresses  in  the  members  of  the  bay 
CD?  There  are  three  cases  to  consider  :  — 

1.  All  wires  intact,  the  C.P.  back,  and  a  factor  of  safety  of  7. 

2.  Front  wire  C  D'  broken,  C.P.  back,  a  factor  of  safety  of 

•66  x  7 

3.  Front    wire   C  D'   broken,  C.P.  forward,   factor   of    safety 

•66  x  7 

To  determine  the  size  of  the  incidence  wire  to  transmit  the 
load  :  the  maximum  load  to  be  transmitted  occurs  with  the 
C.P.  forward  and  has  a  value 

=  sum  of  the  front  reactions  as  far  as  the  bay  c  D 
=  (64  +  155  +  78  +  202  +  176)  x  '68  x  -66  x  7 
=  675  x  '68  x  '66  x  7 
=  2140 

Resolving  this  load  in  the  direction  of  the  incidence  wire  we  have 


Maximum  load  =  -  -—  =2250  Ibs. 
cos  0 

and  the  size  of  the  incidence  wire  must  be  sufficient  to  carry 
this  load. 

Maximum  load  in  the  rear  lift  wire  q  D/.     Considering  the 
cases  enumerated  above  separately  we  have 

1.  Vertical  load  to  be  taken  by  wire 

=  675  x  -79  x  7  =  3740  Ibs. 

2.  (i.)  Load  on  the  rear  frame 

=  3740  x  '66  =  2490  Ibs. 


DESIGN    OF   THE   WINGS  203 

(ii.)  Load  transmitted  from  front  frame  by  incidence  wire 

=  675  x  '21  x    66  x  7  =  66ilbs. 
.-.     Total  load  =  2490  +  66 1  =  3151  Ibs. 
3.  Load  on  rear  frame 

=  675  x  '32  x  '66  x  7  =  zoiolbs. 
Load  transmitted  from  front  frame 

=  675  x  '68  x  *66  x  7  =  2140  Ibs. 
/.     Total  load  =3150  Ibs. 

which  is  nearly  the  same  as  in  the  second  case. 

The  maximum  vertical  load  is  therefore  seen  to  be  3740  Ibs., 
occurring  when  the  C.P.  is  back  and  all  the  wires  are  in.  This 
is  consequently  the  condition  for  which  the  design  must  be 
carried  through,  and  thus  the  design  which  has  just  been  shown 
for  direct  duplication  holds  good  because  the  broken  wire 
does  not  alter  the  maximum  load.  There  will  also  be  an 
additional  load  to  be  carried  by  the  drag  bracing  due  to  the 
horizontal  component  of  the  tension  in  the  incidence  wire. 
To  determine  which  condition  will  produce  the  maximum  load 
in  the  drag  bracing  the  horizontal  reactions  for  each  of  the 
three  cases  must  be  calculated  as  was  done  for  the  lift  bracing, 
and  separate  stress  diagrams  must  be  drawn  from  which  the 
maximum  load  occurring  in  the  drag  bracing  members  is  deter- 
mined. The  direct  end  load  in  the  spars  will  also  be  affected 
by  the  altered  stresses  in  the  drag  bracing ;  and  these  must  like- 
wise be  determined  from  the  stress  diagrams  and  the  maximum 
load  thus  obtained  combined  with  the  correct  bending  moment 
in  the  manner  previously  described. 

Design  of  the  Wing  Ribs.— In  communicating  the  air 
forces  from  the  wing  surface  to  the  spars,  the  ribs  act  as  small 
girders,  and  it  is  necessary  for  design  purposes  to  examine  the 
loads  acting  upon  them  in  flight.  The  load  on  each  rib  is 
obtained  by  determining  the  maximum  load  over  the  wing 
surface  and  dividing  by  the  number  of  ribs  (;/).  This  load  will 
be  the  sum  of  the  reactions  previously  obtained  multiplied  by 
the  factor  of  safety  adopted.  The  distribution  of  the  load  over 
the  wing  section  will  be  similar  to  that  obtained  upon  an  aero- 
foil tested  in  a  wind  tunnel,  and  the  design  of  a  rib  is  based 
upon  the  results  of  pressure  distribution  experiments  such  as 
have  been  described  in  Chapter  III. 

When  applying  these  results  to  a  wing  rib  the  load  curves 
must  be  drawn  for  the  most  unfavourable  conditions  of  incidence 


204  AEROPLANE    DESIGN 

which  are  likely  to  occur.  For  example,  the  maximum  load 
on  the  leading  edge  of  a  wing  will  occur  at  large  angles  of 
incidence,  whereas  the  maximum  load  on  the  rear  portion  of 
the  wing  will  occur  when  the  angle  of  incidence  is  small.  In 
Fig.  149,  obtained  from  pressure  distribution  experiments,  the 
load  curves  over  a  wing  section  for  angles  of  incidence  of  2j-° 
and  T2|°  are  shown.  During  flight  the  wing  loading  W/n  will 
be  the  same  in  each  case.  It  is  therefore  necessary  that  the 
mean  height  of  both  diagrams  should  be  the  same,  hence  the 
pressure  ordinates  have  to  be  altered  in  a  constant  ratio  until 
this  result  is  obtained. 

The  primary  shear  diagrams  are  next  obtained  by  tabular- 
graphic  integration  from  the  load  curves,  commencing  at  the 
front  of  the  section  for  the  12^°  curve  and  at  the  rear  of  the 
section  for  the  2|°  curve  (Fig.  149  b}.  By  further  integration  of 
the  shear  diagram  the  first  bending  moment  curves  are  obtained 
as  shown  in  Fig.  149  (V).  The  position  of  the  spars  having 
been  decided  upon,  the  final  bending  moment  and  shear  force 
diagrams  are  obtained  in  the  following  manner  :  — 

i2j°  incidence.  —  The  centre  of  pressure  corresponding  to  this 
loading  is  at  about  '28  chord. 

Taking  moments  about  B,  see  figure  149  (<:), 
RjO+j')  =  Py 

where  P  is  the  total  load  on  the  rib 
.      R          P}> 

•;  RI  =  JT7 

P  x 


and     R    = 


x  +  y 

The  bending  moment  at  the  rear  spar  due  to  R-^  =  R!  (x  +  y} 

=  Py 

From  B  set  off  a  distance  B  c  to  represent  P^  on  the  same 
scale  as  the  bending  moment  diagram  ordinates.  Join  A  c. 
The  bending  moments  on  the  rib  between  the  spars  are  given 
by  the  difference  in  ordinates  of  the  straight  line  A  C  and  the 
bending  moment  curve.  These  have  been  drawn  to  an  enlarged 
scale  in  Fig.  149  (d\  Similarly  the  final  shear  force  curve  can 
be  drawn  now  that  the  spar  reactions  are  known.  This  is  shown 
beneath  the  bending  moment  curve. 

The  same  procedure  must  be  carried  through  for  the  load 
distribution  at  2j°  incidence,  and  the  final  bending  moment  and 
shear  force  curves  drawn  preferably  on  the  same  base  as  those 


DESIGN    OF   THE   WINGS 


205 


for  the  \2\  incidence,  as  shown  in  Figs.   149  (d  and  e).     The 
curve  which  indicates  the  maximum  bending  moment  or  shear 


.  I2i"  Incidence 


Rib     for    2  Angles  of  Incidence 


Sl">»ar    Force 


Moment 


Rn»l    Bendfng  Moment' 


"  Incidence 


12?  Incidence 


Final  Sheaf  Fcx-ce 


FIG.  149. — Determination  of  B.M.  and  S.F,  Diagrams  for 
Wing  Ribs. 

force  at  a  particular  section  must  be  used  when  designing  the 
rib  at  that  section.  In  developing  the  bending  moment  and 
shear  force  diagrams  along  these  lines,  care  is  necessary  with 


206  AEROPLANE    DESIGN 

the  various  scales  employed  at  each  stage  in  order  that  the  final 
diagrams  may  be  correctly  graduated. 

Having  determined  the  bending  moment  and  shear  force 
over  the  rib,  the  detail  design  follows  in  the  usual  way.  If 
M  be  the  bending  moment  at  the  section  considered,  /  the 
maximum  allowable  stress  in  the  material,  y  the  distance  of  the 
outer  fibre  of  the  rib  from  the  neutral  axis,  and  I  the  required 
moment  of  inertia,  then 


A  suitable  section  with  this  moment  of  inertia  is  then  set 
out.  It  is  customary  to  assume  that  the  rib  flanges  alone  take 
all  the  bending  moment,  while  the  web  takes  all  the  shear,  as 
explained  in  Chapter  IV.,  when  dealing  with  the  stresses  in 
beams. 

The  web  may  be  designed  as  follows  :  — 

Let    d    be  the  depth  of  the  web 
/    be  the  width  or  thickness 
/s  the  safe  shear  stress 

Then  the  shear  load  that  the  web  will  carry 
=  d  x  /  x  /s 

whence  .  _  Shear  force  at  the  section 

~Tx~f~ 

This  relation  fixes  the  thickness  of  the  web,  while  the  wing 
section  itself  fixes  d.  Generally  it  will  be  found  that  in  all 
machines,  except  very  large  ones,  other  practical  considerations 
will  fix  the  sizes  of  the  rib,  which,  if  then  tested  for  shear 
strength,  will  be  found  to  be  amply  strong. 

Wing  Assembly.  —  Several  illustrations  of  typical  aeroplane 
wings  and  their  fittings  have  been  shown  in  the  illustrations 
given  in  this  chapter,  in  order  to  show  the  various  details  and 
the  method  of  assembly.  The  principles  of  construction  are 
similar  in  every  case.  The  wing  is  built  up  on  the  main  spars. 
These  main  spars  are  fixed  at  the  correct  distance  apart,  and 
then  the  ribs,  which  have  been  constructed  on  special  formers 
in  order  to  give  them  the  correct  profile  of  the  aerofoil  selected, 
are  slid  along  the  spars  until  they  reach  their  allotted  place.  A 
distance  of  from  15"  to  20"  is  generally  allowed  between  each 
main  rib,  but  between  the  leading  edge  and  the  front  spar  a 


DESIGN    OF   THE    WINGS  207 

number  of  small  intermediate  ribs  are  fixed  alternately  with  the 
main  ribs  in  order  to  withstand  the  more  intense  pressure  which 
occurs  over  this  portion  of  the  wing.  Each  rib  is  then  glued 
and  screwed  to  the  spars.  If  compression  ribs  are  used  to  take 
the  drag  loads,  they  must  be  strung  on  in  their  correct  order 
with  the  other  ribs  ;  while  if  tubular  or  box  struts  are  used, 
these  are  now  inserted.  A  number  of  small  stringers  are 
threaded  through  the  ribs,  and  serve  to  make  them  more  rigid 
laterally.  The  drag  bracing  wires  can  next  be  attached  to 
their  respective  fittings,  and  the  skeleton  wing  is  then  com- 
plete and  ready,  as  shown  in  Fig.  141,  for  its  covering  of  fabric. 
This  is  bound  round  the  wing  and  sewn  to  the  ribs,  and  then 
covered  with  three  or  four  coats  of  dope,  in  order  to  render  the 
wing  taut  and  weather-proof. 


CHAPTER  VI. 
RESISTANCE  AND  STREAMLINING. 

Resistance. — The  total  resistance  of  an  aeroplane — that  is 
the  force  which  is  balanced  by  the  airscrew  thrust  at  the  flying 
speed  of  the  machine — is  made  up  of  two  parts  : 

1.  The  drag  of  the  wings. 

2.  The  resistance  of  the  remaining  parts  of  the  machine. 

Under  the  second  heading  is  included  the  effect  of  the  inter- 
plane  struts,  the  external  wires,  the  body,  the  chassis,  the  tail, 
and  all  other  fitments  exposed  to  the  wind. 

In  a  normal  machine  flying  at  the  most  efficient  speed,  these 
component  resistances  are  approximately  equal,  so  that  in  de- 
signing an  aeroplane  it  is  as  important  to  assess  the  resistance 
of  the  exposed  parts  correctly  as  it  is  to  know  the  drag  of  the 
wings.  From  one  point  of  view  it  is  more  important,  because, 
with  increase  of  speed,  the  wings  adjust  their  angle  of  incidence 

so   as  to  keep  Ky-AV2  constant,   and    if  the   normal   flying 

o 

angle  is  not  far  from  that  giving  maximum  L/D,  then  the 
increase  of  wing  drag  may  be  small ;  but  since  the  resistance  of 
the  exposed  parts,  other  than  the  wings,  varies  approximately 
as  the  square  of  the  velocity,  a  relatively  small  increase  of 
speed  produces  a  considerable  increase  in  the  magnitude  of  the 
resistance. 

Unfortunately,  it  is  much  more  difficult  to  estimate  the 
second  component  than  it  is  to  calculate  the  first  component,  as 
very  little  is  known  of  the  manner  in  which  the  various  parts  of 
an  aeroplane  interfere  with  one  another.  For  example,  one  part 
may  effectually  screen  another  from  wind  pressure,  or  the  rela- 
tive velocity  with  which  one  part  engages  the  air  may  be  more 
or  less  than  the  velocity  of  the  machine.  Also  the  slipstream 
from  the  airscrew  increases  the  resistance  of  those  parts  of  the 
machine  placed  in  its  stream.  Further,  it  is  necessary  to  correct 
an  estimate  of  the  value  of  the  resistance  of  the  remaining 
parts  of  a  machine  in  the  light  of  the  actual  performance  of  the 
machine  in  flight. 

Of  course,  if  the  complete  aeroplane  were  reproduced  as  a 
scale  model,  it  would  be  possible  to  predict  this  body  resistance 
accurately  from  wind  tunnel  tests,  but  the  construction  of  the 
.model  is  obviously  a  difficult  and  at  the  same  time  an  expen- 


Reproduced  by  courtesy  of  Messrs,  Handley  Page,  Ltd. 

FIG.  151. — Front  and  Rear  Views  of  ¥-1500  with 
Wings  folded  back. 

Facing  page  208. 


RESISTANCE    AND    STREAMLINING  209, 

sive  matter.  The  designer  should,  therefore,  try  to  arrange  for 
the  reduction  of  the  second  component  to  an  absolute  minimum. 
In  so  doing  he  will  be  guided  by  knowledge  of  the  resistance 
of  bodies  of  various  shapes  placed  in  the  air-stream  of  the  wind 
tunnel  under  more  simple  conditions. 

A  brief  consideration  of  the  following  example  will  empha- 
sise the  importance  of  concentrating  on  minimising  the  second 
component,  and  will  also  show  that  if  considerable  weight  has  to 
be  added  in  order  to  reduce  the  resistance  of  a  given  part,  it 
may  frequently  be  an  advantage  to  tolerate  this  additional 
weight.  Say  a  complete  machine  has  a  gliding  angle  of  one  in 
eight.  This  means  that  the  overall  efficiency  or  ljft/drag  ratio 
of  the  machine  is  8.  Now,  if  the  second  component  can  be 
reduced  by  I  Ib.  by  some  means,  then  the  machine  will  lift 
another  8  Ibs.  for  the  same  speed.  The  overall  efficiency  of  a 


FIG.  152. — Flow  past  a  FIG  153. — Flow  past  a  Streamline 

Flat  Plate.  Shape. 

machine  must  be  borne  in  mind,  therefore,  when  comparing 
struts,  bodies,  etc.,  of  different  resistances  and  different  weights. 
It  follows  from  this  that  the  more  efficient  an  aeroplane,  the 
more  it  pays  to  improve  its  efficiency. 

The  resistance  of  any  body  placed  in  a  current  of  air  (this  is, 
of  course,  equivalent  to  its  resistance  to  motion  through  still  air) 
is  composed  of  two  parts,  namely  : 

1.  The  excess  of  air  pressure  in  front  of  the  body  over  that 

behind  it,  and 

2.  The  skin  friction. 

It  is  shown  subsequently  that  the  amount  of  skin  friction  is 
small  where  the  surface  is  small,  and  the  considerable  resistance 
therefore  of  some  small  bodies  is  almost  wholly  due  to  the  first 
part.  This  excess  of  pressure  is  caused  by  a  discontinuity  of 
flow  due  to  the  abruptness  of  the  body  giving  rise  to  a  *  dead- 
air'  region  of  diminished  pressure  in.  the  rear  of  the  body,  and 
to  increased  pressure  on  the  face  of  the  body  owing  to  the 
forward  velocity  of  the  air  being  reduced.  This  point  will  be 
made  clear  by  reference  to  Fig.  152,  which  shows  the  flow  of 
air  past  a  normal  flat  plate.  At  B  one  streamline  is  evidently 


210  AEROPLANE    DESIGN 

brought  to  rest,  its  velocity  head  being  entirely  converted  into 
pressure,  but  the  pressure  thus  set  up  will  evidently  diminish 
towards  the  edges  of  the  plate  as  the  stream  divides  to  flow 
round  the  plate.  A  is  the  dead-air  region  of  diminished  pressure. 

In  seeking  to  diminish  resistance,  the  principle  is  to  elimi- 
nate as  far  as  possible  this  region  of  'dead  air/  and  to  make 
the  air  flow  round  the  body,  thus  preventing  any  discontinuity 
in  the  flow.  The  body  is  then  said  to  be  '  streamlined,'  that  is, 
it  possesses  a  contour  that  the  streamlines  of  flow  can  easily 
follow.  Its  limiting  resistance  is  then  the  frictional  resistance  of 
the  air  flowing  over  the  surface  ;  and  as  this  is  a  small  quantity, 
the  saving  of  resistance  which  can  be  obtained  by  efficient  stream- 
lining is  large.  Taking  again  the  example  of  the  normal  flat 
plate  of  circular  section,  it  is  found  necessary,  in  order  to  stream- 
line it,  to  fit  on  both  a  nose  and  a  tail,  so  that  we  arrive  at  a 
form  somewhat  similar  to  that  of  a  fish  or  a  bird.  The  more  or 
less  pointed  nose  eases  the  streamlines  away  from  the  disc 
without  materially  checking  the  flow,  and  a  longer  more  or  less 
pointed  tail  eases  them  back  again  after  passing  the  plate  or 
disc. 

Fig-  J53  depicts  the  flow  past  the  plate  streamlined  by 
the  addition  of  a  nose  and  a  tail.  As  will  be  seen,  the  region  B 
has  been  eliminated,  and  the  region  A  considerably  reduced. 

Variation  from  the  (V2)  Law. — The  resistance  due  to 
excess  of  air  pressure  varies  with  the  square  of  the  wind 
velocity  (V),  while  that  due  to  skin  friction  varies  as  V1'85.  So 
long  as  the  skin  friction  is  small  in  amount  in  comparison  with 
the  resistance  due  to  disturbance  of  the  streamline  flow,  then 
the  total  resistance  varies  very  approximately  as  the  square  of 
the  velocity  (V).  In  the  case  of  a  good  streamline  form,  how- 
ever, where  the  skin  friction  is  comparable  with  the  resistance 
due  to  the  excess  of  air  pressure,  it  may  confidently  be  antici- 
pated that  the  total  resistance  will  vary  according  to  an  index 
of  V  much  less  than  2.  Hence  if  it  is  assumed  that  the  resist- 
ance of  a  streamline  section  is  given  by  the  general  formula 
R  =  K  A  V2,  then  the  coefficient  K  will  diminish  as  the  velocity 
is  increased.  Experiments  carried  out  on  strut  sections  by 
Eiffel  and  the  National  Physical  Laboratory  have  shown  that 
this  is  actually  the  case. 

Fig.  154  gives  the  results  of  tests  carried  out  by  Eiffel  on  the 
three  strut  sections  shown.  As  will  be  seen,  the  drag  coefficient 
diminishes  in  each  case  with  increase  of  speed,  but  with  the 
more  perfect  streamline  shapes  the  diminution  is  very  much 


RESISTANCE   AND   STREAMLINING 


21 


greater  than  with  those  of  a  more  imperfect  form.  This 
reduction  of  resistance  at  high  velocities  should  be  taken 
account  of  when  estimating  the  resistance  of  good  streamline 
shapes.  Also  in  making  a  comparison  between  the  efficiency  of 
such  shapes  tested  at  different  speeds,  an  allowance  should  be 
made  for  this  effect. 

The  advantage  to  be  derived  in  making  a  strut  section  of 
good  streamline  shape  is  well  illustrated  in  Fig.  154,  for  it  will 
be  seen  that  the  resistance  of  strut  No.  3  is  four  or  five  times 
greater  than  that  of  struts  Nos.  I  and  2  at  the  speeds  of  flight 
corresponding  to  those  used  in  normal  flying  conditions. 


FIG.  154. — Variation  of  Drag  with  Change  of  Velocity. 


Streamlining. — The  designing  of  a  good  streamline  form  is 
an  exceedingly  delicate  matter.  The  greatest  scope  is  offered 
with  airship  bodies.  The  fuselage  of  a  tractor  aeroplane  and 
the  floats  of  a  seaplane  would  offer  an  equally  good  field,  but 
unfortunately  the  former  has  %  to  accommodate  an  engine,  and 
the  latter  have  to  be  capable  of  easily  leaving  the  water,  both  of 
which  considerations  result  in  a  modified  form.  A  fair  field  is, 
however,  offered  by  the  various  struts  of  an  aeroplane,  and  it  is 
convenient  to  examine  the  matter  from  this  point  of  view, 
although,  of  course,  most  of  the  following  remarks  apply  almost 
equally  well  to  any  other  solid  body.  Increase  of  resistance  for 
small  increases  in  size  varies  approximately  as  the  increase  of 
projected  area  upon  a  plane  normal  to  the  wind.  It  must  be 


212  AEROPLANE    DESIGN 

borne  in  mind  that  a  very  large  change  in  size  may  involve  a 
scale  effect  only  to  be  investigated  by  experiment. 

The  strength  of  a  strut  depends  on  the  moment  of  inertia  of 
its  section.  The  form  of  section  giving  a  maximum  value  of 
this  with  minimum  weight  is  the  circular  section  of  hollow  form. 
The  circle  is  a  partly  streamlined  form  of  section,  the  resistance 
being,  according  to  Eiffel,  some  60%  of  the  resistance  of  a  flat 
rectangular  plate  of  the  same  dimensions,  for  sizes  usually 
obtaining  with  aeroplane  struts.  A  further  large  reduction  in 
resistance  may  be  obtained  by  simply  elongating  the  circle  in 
the  direction  of  motion  into  an  ellipse,  that  is,  by  giving  the 
section  a  '  fineness  ratio.'  Fineness  ratio  is  defined  as  the  ratio 


o  oo 


DC  HavilUod 


FIG.  155. — Strut  Section. 

of  the  length  of  the  section  to  its  maximum  breadth.  The 
saving  to  be  effected  in  this  way  is  about  S°%  °f  the  resistance 
of  the  cylinder  when  the  fineness  ratio  is  2,  and  a  further  IS°/0 
can  be  obtained  by  increasing  the  fineness  ratio  to  5.  For  a 
really  good  shape  it  is  best  to  use  a  fineness  ratio  of  about  3,  or 
just  a  little  over,  and  to  keep  the  maximum  thickness  well 
towards  the  nose,  say  one-third  of  the  length  of  the  section 
back,  and  to  keep  the  run  of  the  '  contour '  fairly  flat  at  about 
this  point.  It  is  easy  to  produce  a  strut  on  these  lines  having  a 
resistance  of  only  15%  of  the  equivalent  cylinder,  or  only  9% 
of  the  equivalent  rectangular  plane.  It  is  of  practically  no 
importance  whether  the  ends  of  the  section  are  pointed  or  not, 
and  it  is  usually  most  convenient  to  have  well-rounded  ends. 

An  instructive  series  of  tests  was  carried  out  upon  a  number 
of  struts  by  the  N.P.L.  in  order  to  determine  the  best  form  of 


RESISTANCE   AND    STREAMLINING  213 

strut  when  taking  into  consideration  both  weight  and  strength 
as  well  as  resistance.  Some  of  the  sections  are  shown  in 
Fig.  155,  and  of  these  the  Bleriot,  Farman,  and  De  Havilland 
were  taken  from  struts  in  use  on  machines.  The  results  are  set 
out  in  Table  XXIX. 

It  will  be  noted  that  there  is  a  considerable  range  of  shape  of 
section  for  which  the  equivalent  weights  vary  but  little,  while 
some  of  those  sections  which  have  been  used  on  actual  machines 
have  an  equivalent  weight  of  from  150  to  180  Ibs.  The  substi- 
tution of  struts  of  'Beta'  section  for  those  on  the  Farman 
biplane  would  have  enabled  it  to  carry  79  Ibs.  more  useful  load, 
without  any  addition  to  the  horse  power  required. 

TABLE  XXIX. — RESISTANCES  OF  STRUTS. 


Resistance  of         Weight  of  100  ft.          Maximum        Equivalent  weight 
100  ft.  of  strut                 of  strut,                 thickness  for              of  struts  of 

Type  of  strut.                @  60  ft  /sec.                  maximum            equal  strength.        equal  strength. 

Lbs. 

thickness  i". 

Inches. 

Lbs. 

Circular,  i"  diam. 

43 

...           23-4           ... 

I  '005 

295 

De  Havilland    ... 

25'5 

29-2 

0'99 

1  80 

Farman   .. 

22-9 

36'0 

0-905        ... 

'54 

Bleriot    

237 

...           37'2           ... 

0-92 

162 

Baby       

7'9 

59'4 

0-822        ... 

79 

Beta       

6-9 

88-1 

0718       ... 

75 

B.F.  34  

7-2 

...     133-0       ... 

0'65 

84 

B.F.  35  

6'3 

...     128-0 

0-677        ••• 

84 

The  effect  of  yawing  is  to  increase  the  resistance  of  a  strut 
considerably  on  account  of  the  additional  side  force  exerted  by 
the  air. 

Inclination  of  Struts. — An  investigation  into  the  effect  of 
inclining  struts  to  the  air  stream,  such  as  will  occur  for  example 
in  the  struts  of  staggered  machines,  has  also  been  made.  It  was 
found  that  for  streamline  shapes  there  is  very  little  alteration  in 
the  resistance,  but  that  for  blunt-nosed  sections  the  resistance 
was  greatly  reduced  owing  to  the  increased  length  of  section  in 
the  air  stream. 

Resistance  of  the  Body  or  Fuselage. — Since  this  forms 
the  largest  item  in  the  consideration  of  resistance  it  will  be  con- 
sidered at  some  length,  so  that  when  a  fuselage  of  a  new  design 
has  been  drawn  out,  an  estimate  can  be  made  of  its  probable 
resistance.  The  resistance  of  the  body  will  vary  approximately 
as  the  square  of  the  velocity,  and  as  has  already  been  observed 
since  the  drag  of  the  wings  remains  practically  constant  for 


2I4 


AEROPLANE    DESIGN 


various  flight  speeds,  the  question  of  the  resistance  of  the  body 
relative  to  that  of  the  wings  becomes  of  increasing  importance 
as  the  speed  of  flight  is  increased. 

This  item  must  of  course  be  reduced  as  much  as  possible, 
and  more  especially  is  this  necessary  in  the  case  of  very  high- 
speed machines.  The  necessity  for  adopting  good  streamline 
shapes  is  at  once  evident,  and  it  is  to  the  realisation  of  this  fact 
in  practice  that  the  modern  development  of  high-speed  machines 


MM. 


N?3. 


/1"~T 

t 

4-7£" 

4-1 

^f-T 

I 

! 

-O 

1  *  01  -* 

t 

NTS. 


FIG.  156. — Shapes  used  by  Eiffel  in  determining  best  form 
of  fuselage.   ' 

is  to  a  large  extent  due.  A  convenient  method  of  comparing 
the  resistance  of  various  types  of  fuselages  is  to  express  these 
resistances  in  terms  of  a  flat  plane  normal  to  the  wind.  For  an 
efficient  type  of  body  the  equivalent  normal  plane  should  be  of 
a  very  much  smaller  cross  section  than  the  maximum  cross 
section  of  the  body.  In  many  cases  in  practice,  however,  the 
resistance  of  the  body  is  more  than  half  the  resistance  of  the 
equivalent  flat  plane,  but  with  efficient  design  the  maximum 


RESISTANCE    AND    STREAMLINING  215 

resistance  should  not  be  more  than  one  quarter  (25  per  cent). 
In  order  to  obtain  such  a  desirable  result  it  is  necessary  to  avoid, 
as  far  as  is  practically  possible,  all  projections  and  corners  likely 
to  cause  disturbances  in  the  air  flow.  All  members  exposed  to 
the  air  stream  must  be  *  faired  '  to  a  streamline  shape,  a  process 
which  calls  for  the  exercise  of  a  considerable  amount  of  care  and 
patience,  but  which  is  amply  repaid  in  the  reduced  resistance 
obtained. 

In  the  absence  of  definite  figures  relating  to  the  particular 
machine  under  design,  the  calculation  of  body  resistance  requires 
the  computation  of  the  resistance  of  each  element,  for  which 
purpose  it  is  convenient  to  have  the  tabulated  results  of  the 
resistance  of  different  kinds  of  fuselages,  wires,  chassis,  wheels, 
and  other  components.  Most  of  the  data  available  for  this 
purpose  is  the  outcome  of  experiments  carried  out  by  M.  Eiffel 
and  by  the  National  Physical  Laboratory.  Some  experiments 
carried  out  by  Eiffel  upon  the  shapes  shown  in  Fig.  1 56  will 
form  a  very  useful  introduction  to  this  subject.  These  shapes 
consist  of  a  nose,  a  cylindrical  centre  portion,  and  a  conical  tail. 
The  results  of  the  tests  may  be  summarised — 

(i)  The   blunter   the   nose   the   greater   is    the    resistance. 

N.B. — Nose  of  section  I  is  of  streamline  form. 
(ii)  For  the  same  nose  and  tail  the  resistance  diminishes  as 

the  length  of  the  central  portion  is  reduced, 
(iii)  Diminution  in  the  length  of  the  tail  leads  to  a  slightly 

increased  resistance. 
(iv)  With   streamline  shapes  the  resistance   varies   with  the 

velocity  according  to  an  index  less  than  2,  the  skin 

friction   forming  a  considerable  portion  of  the  total 

resistance. 

TABLE  XXX. — RESISTANCE  COEFFICIENTS  FOR  FUSELAGE  SHAPES. 

Equivalent  normal  plane  coefficients. 


Body. 

32-8  f.p.s. 

65*6  f.p.s. 

98-4  f.p.s. 

131-2  f.p.s. 

I  

0*015 

0*0139 

0*013 

0"OI2 

II  

0*0147 

0*0141 

0-0133 

0*0121 

Ill  

o  170 

0*0161 

0*015 

00135 

IV  

0*0132 

0*0123 

0*0115 

o'oio3 

V.  Round  end 

foremost... 

0-0152 

0*0143 

0-0137 

o  0103 

V.  Round  end 

behind    .  .  . 

0*0182 

o  0167 

0-0164 

0*0103 

N.B.  —  Observe  that  the  resistance  coefficient  diminishes  consider 
ably  as  the  air  speed  increases. 


2l6 


AEROPLANE    DESIGN 


Turning  from  the  general  question  of  the  resistance  of  bodies 
made  up  of  geometrical  solids,  the  question  of  the  resistance  of 


Square 
and 
Circular 


Square  bod^     wif>>      fore   and 
afr   Mind    shields 


(d  ^    Circular    bod^      wirti 
and    afr     wind 


FIG.  157. — Aeroplane  Bodies. 


various  types  of  fuselages  met  with  in  aeronautical  practice  will 
next  be  considered. 


RESISTANCE   AND    STREAMLINING 


217 


Aeroplane  Bodies.— An  investigation  was  made  by  the 
N.P.L.  into  the  effect  of  various  modifications  of  the  form  of 
aeroplane  bodies  upon  the  resulting  forces  and  moments. 


—  0.25 


35- 


Angle      of    Yaw 

FIG.  158. — Comparison  of  Bodies  of  related  Cross  Section. 


A  comparison  was  first  made  of  bodies  of  square  and  circular 
cross  section,  after  which   these  bodies  were  modified  by  the 


2l8 


AEROPLANE    DESIGN 


addition  of  wind  shields  of  various  types.  For  the  first  com- 
parison the  square  section  body  was  taken  as  the  basis.  Then 
the  relation  between  the  three  bodies  was  such  that  the  circular 
sections  at  all  points  along  bodies  were  respectively  the  in- 
scribed and  circumscribed  circles  of  the  square  section.  The 


SQUARE:     CROSS    SECTION 


FIG.  159. 

scheme  is  shown  at  the  top  of  Fig.  .158.  Throughout  this 
investigation  it  was  assumed  that  the  position  of  the  centre  of 
gravity  was  5*8  inches  behind  the  nose  of  the  body,  this  figure 
being  taken  as  a  fair  mean  position  after  a  consideration  of 
a  large  number  of  types  of  existing  machines. 


RESISTANCE   AND    STREAMLINING 


219 


The  experimental  results  are  shown  plotted  in  Fig.  158,  and 
it  is  somewhat  surprising,  taking  into  consideration  the  available 
amount  of  stowage  space  for  engines,  etc.,  the  greater  con- 


CIRCULAR    CROSS  SECTION 


FIG.  1 60. 


venience  of  attachment  of  such  details  as  the  wings  and  chassis, 
and  the  much  greater  ease  with  which  it  can  be  constructed,  that 
the  square  section  should  prove  to  be  the  best  type  of  body  for 


220 


AEROPLANE    DESIGN 


general  use.     Ip  order  to  obtain  the  same  amount  of  stowage 
space  it  would   be  necessary  to  go  to  the  size  of  the  circum- 


SQUARE:  CROSS  SECTION 


Wind    Spfced 


Y(0 


N(b) 


5*  10°  15*  E0°  25°  T>0~ 

Angle    of     Yawfyr) 

• 

FIG.  161. 

scribing  circular  section,  and,  as  will  be  seen  from  Fig.  158,  while 
this  body  is  nearly  as  good  as  the  square  section  generally,  in 


RESISTANCE   AND    STREAMLINING 


221 


the  case  of  the  Yawing  Moment  curve  near  the  origin  there  is 
a  much  greater  slope  for  the  circular  section,  so  that  a  much 
larger  rudder  would  be  necessary  in  order  to  counteract  the 
negative  righting  moment  due  to  the  body.  Moreover,  the 


CIRCULAR    CROSS    SECTION 


0° 


Wind  Spc  d     40  f  p.S 


Y(d)' 


Y(aV 


FIG.  162. 


square  section  body  possesses  a  much  greater  value  for  the 
lateral  force  than  the  circumscribing  circular  section,  which  in 
practice  is  equivalent  to  an  addition  to  the  area  of  the  fin,  and 
acts  as  a  corrective  to  sideslip. 


222 


AEROPLANE    DESIGN 


The   models   for   the  general   series  of  tests  are  shown   in 
Fig.   157,  namely, 

(a)  Perfectly  plain  body— square  and  circular  sections  ; 

(b)  Cockpit  and  pilot  added — square  and  circular  sections  ; 

(c)  Cockpit,  pilot,  fore  and  aft  wind  shields  added — square 

section  ; 

(d)  Cockpit,  pilot,  fore  and  aft  wind  shields  added — circular 

section. 

Tests  were  also  carried  out  upon  models  possessing  a  rear  wind 
shield  only,  but,  as  was  to  be  expected,  the  results  showed  that 
wind  shields,  both  fore  and  aft,  are  preferable  in  all  respects. 


The  curves  plotted  in  Figs.  159-162  show  that  small  modi- 
fications in  the  shape  of  the  bodies  do  not  affect  either  the  forces 
or  moments  to  any  great  extent,  with  the  one  exception  of  the 
longitudinal  force.  As  will  be  seen  from  these  figures,  this 
force  is  particularly  sensitive  to  small  changes  of  shape,  more 
especially  so  at  large  angles  of  yaw.  The  designer  should 
therefore  aim  at  keeping  this  longitudinal  force  as  low  as 
possible,  while  giving  the  pilot  as  much  protection  as  possible 
from  the  wind,  consistent  with  a  good  forward  view.  The 
development  of  a  satisfactory  transparent  screen  totally  en- 
closing the  pilot  would  be  of  considerable  utility  in  ensuring 
his  comfort  upon  long-distance  journeys,  and  of  distinct  advan- 
tage from  an  aerodynamical  standpoint,  but  mechanical  or  other 
means  would  have  to  be  devised  to  keep  it  clear  in  all  weathers. 


RESISTANCE    AND    STREAMLINING  223 

Deperdussin  Monocoque  Fuselages. —  Eiffel  has  tested 
two  types  of  fuselage  similar  to  those  shown  in  Figs.  163  and 
164.  It  will  be  seen  that  the  bodies  differ  in  the  arrangement 
of  the  nose  portion,  the  one  being  fitted  with  a  rotary  engine 
and  top  cowl  only  ;  while  in  the  other  the  engine  was  totally 
enclosed  save  for  a  small  aperture  between  the  propeller  boss 
and  cowl  to  admit  the  cooling  air.  The  models  were  to  one- 
fifth  scale  and  of  the  following  dimensions  : — Length,  2*94  ft.  ; 
diameter  of  No.  I  (Fig.  163),  0*525  ft.;  diameter  of  No.  2  (Fig.  164), 
0-588  ft.  The  tests  were  made  at  speeds  varying  from  80  to  90 
f.p.s.  In  the  first  series  of  tests  no  airscrews  were  fitted  to  the 
models,  and  the  results  were  as  follows  : — 

TABLE  XXXI.— MONOCOQUE  FUSELAGES  WITHOUT  AIRSCREWS. 

Fuselage.  Resistance  at  60  m.p.h. 

No.   I  ...  ...  ...  ...         22*6  Ibs. 

No.  2  ...         ...         ...         ...       19*0  Ibs. 

In  the  second  series  of  experiments  made  upon  these  models, 
airscrews  were  fitted  and  allowed  to  rotate  with  the  engine 
under  the  influence  of  the  moving  air,  the  conditions  thus 
approximating  to  those  occurring  during  a  glide  with  the 
engine  switched  off  but  rotating.  The  results  were  ^as 
follows  : — 

TABLE  XXXII.  — MONOCOQUE  FUSELAGES  WITH  AIRSCREWS. 

Type  of  fuselage.  Resistance  at  60  m.p.h. 

No.  i  65     Ibs. 

No.  2  43-8  Ibs. 

It  will  be  seen  that  the  introduction  of  the  airscrew 
increases  the  resistance  very  considerably.  This  is  due  to  the 
increased  pressure  on  the  fuselage  resulting  from  the  airscrew 
wake  and  to  the  disturbance  in  the  air  flow  over  the  entire 
surface. 

Fig.  165  represents  another  type  of  body  in  which  the  model 
was  fitted  both  with  a  tail  plane  and  an  under-carriage,  and  was 
to  one-twelfth  scale.  The  resistance  of  the  model  was  found  to 
be  0*1365  Ibs.  at  30  m.p.h.  The  corresponding  resistance  of  the 
full-size  body — 24*5  ft.  long — complete  is  218  Ibs.  at  100  m.p.h. 

B.E.  2  and  B.E.  3  Fuselages. — A  very  complete  investiga- 
tion was  made  by  the  National  Physical  Laboratory  into  the 
forces  and  moments  acting  upon  the  models  shown  in  Figs.  166 
and  167.  Since  the  results  are  also  of  great  utility  in  considering 
questions  of  stability  in  addition  to  their  value  in  estimating 
body  resistance,  they  will  be  given  in  entirety. 


224 


AEROPLANE   DESIGN 


Scale    of    Mode!       w- 
Figs.  1 66  and  167. — Forces  and  Moments  on  Model  Fuselages. 

Measurements  were  made  of — 

(i.)  Lift  and  drag  for  various  pitching  angles  with  zero  angle 

of  yaw ; 
(ii.)  Pitching  moment  about  a  horizontal  axis  perpendicular 

to  the  wind,  with  zero  angle  of  yaw  ; 

(Hi.)  Drag,  lateral  force,  and  yawing  moment,  about  a  vertical 
axis  for  different  angles  of  yaw  with  the  pitching  angle 
zero. 


RESISTANCE   AND    STREAMLINING 


225 


The  results  are  exhibited  graphically  in  Fig.  168.  It  will 
be  noted,  in  the  case  of  the  longitudinal  force  curves,  how  the 
longitudinal  force  rises  rapidly  with  increase  of  angle  of  yaw  in 
the  case  of  the  B.E.  2  body.  This  is  probably  due  to  the  pro- 
jecting head  and  shoulders  of  the  aviators  when  there  is  a  small 
angle  of  yaw.  In  the  B.E.  3  there  is  no  such  effect,  and  the 
longitudinal  force  varies  very  little  for  small  angles  of  yaw. 
The  curves  show  that  the  B.E.  3  body  is  of  a  much  better  form 
than  the  B.E.  2,  its  drag  at  zero  angle  being  only  half  that  of  the 


Pitching     Angle 


Pitching    Angle 

FIG.  1 68. — Forces  and  Moments  on  B.E.  Fuselages. 

latter  in  the  same  position.  The  moment  curves  show  that  in 
all  cases  the  bodies  are  unstable  in  their  symmetrical  position 
if  supported  at  the  C.G.,  that  is,  for  small  angular  displacements 
there  is  a  moment  tending  to  increase  the  angle  of  displacement. 
The  wind  speed  throughout  all  these  tests  was  30  f.p.s. 

A  further  series  of  experiments  was  carried  out  on  the  two 
models  shown  in  Figs.  169  and  170.  Both  these  models  were 
tested  with  and  without  the  rudder,  and  readings  were  taken  of 
the  lateral  force,  drag,  and  yawing  moment  for  various  angles  of 
yaw.  After  these  tests  had  been  completed  on  the  model  shown 
in  Fig.  169,  the  recesses  round  the  crank  case  were  faired  with 


226 


AEROPLANE    DESIGN 


plasticine  and  the  drag  at  zero  yawing  angle  determined.  The 
drag  was  found  to  be  reduced  from  0*016  Ib.  to  0*0148  lb.,  a 
reduction  of  7*5%. 

The  general  results  indicate  that  model,  Fig.  169,  is  slightly 
better  than  the  B.E.  2,  but  not  so  good  as  the  B.E.  3  body.  The 
curves  of  model,  Fig.  170,  are  similar  to  the  others  in  general 
form,  the  chief  difference  being  in  the  curve  of  yawing  moment 
without  rudder.  For  this  body  a  restoring  moment  is  obtained 


Rg.  170 


for  displacements  from  the  symmetrical  position  as  regards 
yawing  motion  about  the  C.G.  This  is  probably  due  to  the  two 
small  fins  just  in  front  of  the  rudder  itself,  which  were  not 
removed  in  the  test  without  the  rudder. 

In  Table  XXXI II.  the  resistance  in  pounds  of  the  four  full- 
sized  bodies  at  60  m.p.h.  without  rudder  or  elevator  planes  is 
given.  The  four  bodies  are  not  very  different  in  over-all  length, 
hut  in  order  to  allow  for  this  difference  the  value  of  the  resist- 
ance, divided  by  the  square  of  the  over-all  length,  has  been 
given.  The  figure  so  obtained  is  a  fair  criterion  of  the  relative 


FIG.  171. 
LONGITUDINAL  &c  L/KTEIRAL  FORCES  ON  MODELS 


il 


•02. 


-01 


\ 


of  Yav/ 


I  r  15  2  Q  f. 


\ 


Rudder  in  pos1? 


I 

-0-4 


-•03 


~<X  -<M 


-l>  -10 


Force 


.._.b.A"B^ 


WfH>  Rluddcr  in  poe^ 
Rudder 


-0-1 


-02 


228  AEROPLANE   DESIGN 

efficiency  of  the  bodies  as  regards  resistance  in  the  normal  flight 
position.  The  actual  resistances  were  calculated  by  assuming 
the  drag  to  vary  as  the  square  of  the  velocity  and  as  the  square 
of  the  linear  dimensions. 

TABLE  XXXIII.  —  COMPARISON  OF  FOUR  FUSELAGE  BODIES. 

Body.  Drag  at  60  m.p.h.  Drag/Length2. 

B.E.  2  ...         ...       54*0  Ibs.  ...         ...       o'io2 

B.E.  3  ...         ...       25*8    „  ...         ...       0*041 

Model  4  ......       35-3    „  ......       0-080 

Model  5  ......       18-4    „  ......       0-054 

Resistance  of  Wires.  —  The  results  of  a  large  number  of 
tests  show  that  the  resistance  of  a  wire  may  be  expressed  in 
the  form, 

R  =  K^  V2        ...............  Formula  68 


where     d  =  the  diameter  of  the  wire, 

V  =  the  velocity  of  the  air  relative  to  the  wire  in  feet  per  second, 
R  =  the  resistance  per  foot  run, 

K  =  a  multiplying  constant,  which  depends  upon  the  product 
dV,  in  accordance  with  the  principle  of  dynamic 
similarity. 

For  values  of  dV  less  than  0*15,  K  decreases  with  increase 
of  */V,  and  for  values  of  d^J  greater  than  0*15,  K  increases 
with  dV.  It  is  with  the  latter  portion  that  we  are  chiefly  con- 
cerned in  aeronautics.  Table  XXXIV.  gives  the  values  of  K 
for  increasing  values  of  d  V,  and  is  taken  from  results  of  tests 
at  the  N.P.L. 

TABLE  XXXIV.  —  VALUES  OF  K  WITH  INCREASE  OF  dV. 

dV        0-5  1*0  1*5  2'o  2-5  3*0 

K         *ooi2       '0013       '00137       '00141       '00144       '00145 

These  experiments  covered  a  range  of  speed  of  from  9  to 
25  feet  per  second,  and  the  diameters  of  the  wire  varied  from 
•04"  to  0-2  5  ". 

More  recent  experiments  at  the  N.P.L.  have  been  made  at 
speeds  up  to  50  feet  per  second  and  upon  wires  up  to  f  "  in 
diameter.  The  results  are  shown  graphically  in  Fig.  172,  where 
the  value  of  the  constant  K  is  plotted  against  the  product  d  V 
in  F.P.S.  units. 


RESISTANCE   AND    STREAMLINING 


229 


For  example,  to  find  the  resistance  of  a  J"  wire  at  100  m.p.h., 
d      =  "25"  =  '02083' 
V     =  100  m.p.h.  =  1467  f.p.s. 
f/V  =  146*7  x  '02083  =  3'°6 

From  Fig.  172,  the  value  of  K  corresponding  to  3*06  =  '00145. 
.'.  Resistance  of  £"  wire 

=  '00145  x  '02083  x  J46'7  x  J46'7 
=  0*65  Ib.  per  foot  run 


0  5  (-0 

d  V      it 


15  20 

Fbof    Secorjd      Uijite 


FIG.  172. — Values  of  k  with  increase  of  //V 

The  values  given  in  Table  XXXIV.  are  for  smooth  wires, 
For  stranded  cables  or  ropes  these  values  must  be  increased  20%. 

If  the  struts  or  wires  are  inclined  to  the  direction  of  motion 
of  the  air,  the  resistance  may  be  very  much  diminished  owing  to 
the  change  in  shape  of  section,  as  the  following  table  shows. 

TABLE  XXXV. — RESISTANCE  OF  INCLINED  STRUTS  AND  WIRES. 
Inclination  of  strut 


to  wind 


80° 


6oc 


90         60  70         00          50  40  30 

Percentage  of  Normal  Resistance  for  Constant  Projected  Length. 
Circular  section  ...      100      96         88      76       61         45          31 
Streamline  section      100      97^5      91      83      70^5      55*5      45*5 


20 

21 

44 


230 


AEROPLANE   DESIGN 


The  percentage  resistance  for  the  struts  at  all  angles  is  given 
in  terms  of  their  resistance  when  normal.  The  last  line  shows, 
as  was  to  be  expected,  that  for  a  streamline  strut  or  wire  there 
is.  not  such  a  large  gain  due  to  inclination  as  for  a  strut  or  wire 
of  circular  section. 

Resistance  of  Flat  Plates. — The  resistance  of  a  flat  plate 
normal  to  the  wind,  apart  from  scale  effect,  depends  upon  the 
compactness  of  its  outline.  For  example,  the  best  form  of 


FIG.  173. — Wind  Forces  on  Wheel  of  Landing  Chassis. 

outline  is  a  circle,  while  the  worst  form  is  one  having  many 
re-entrant  angles.  The  following  formula  by  the  N.P.L.  gives 
the  resistance  of  square  plates  for  values  of  V  L  between  I  and 
350,  where  V  is  the  velocity  in  feet  per  second,  and  L  is  the 
length  of  the  side  in  feet. 

R  =  -00126  (VL)2  +  -0000007  (VL)3    Formula  69 

For  rectangular  plates  the  results  obtained  by  this  formula  must 
be  corrected  by  the  use  of  the  factors  in  Table  XIV. 

Resistance  of  Landing  Gear. — When  designing  a  landing 
gear,  care  should  be  taken  that  all  struts  and  tubes  are  enclosed 


RESISTANCE   AND   STREAMLINING  231 

in  a  streamline  fairing  in  order  to  cut  down  the  resistance  as  far 
as  possible.  «, 

M.  Eiffel  has  measured  the  resistance  of  several  full-sized 
landing  chassis  wheels,  the  results  of  which  are  embodied  in 
Table  XXXVI.  below. 

TABLE  XXXVI. — RESISTANCES  OF  LANDING  WHEELS. 

Dimensions  of  T>     •  f  Equivalent 

Type  of  wheel.  tyre  Kesistanc.          normal    ^ 

(mms.)  at82f.p.s.  const£nt. 

Deperdussin          ...       725  x  65  ...        3*88  ...        0*92 

Farman  (uncovered)       610x77  •••       4'J9  •••        I'°° 

Farman  (covered)...       610  x  77  ...        2^07  ...        0*49 

Dorand       ...          ...        530  x  80  ...        2*57  ...        0*68 

Astra  Wright         ...       450  x  53  ...        1*27  ...        o'8o 

It  will  be  observed  from  this  table  that  the  effect  of  covering 
the  Farman  wheel  is  to  reduce  its  resistance  by  $0%.  Tests  at 
the  National  Physical  Laboratory  to  find  the  resistance  and  the 
lateral  force  upon  the  wheel  shown  in  Fig.  173  gave  the  results 
shown  in  that  figure. 

Effect  of  Airscrew  Slip  Stream. — The  effect  of  the  air- 
screw slip  stream  upon  those  members  situated  within  it  is  to 
increase  the  velocity  of  the  air  impinging  upon  them.  This 
means  a  corresponding  increase  in  their  resistance,  which  must 
be  allowed  for  when  making  an  estimate  of  their  resistance  and 
the  total  resistance  of  the  machine.  The  slip  stream  effect  is 
not  easy  to  estimate,  the  relative  increase  in  resistance  being 
much  greater  at  low  speeds  than  at  high.  The  slip  stream  is 
regarded  by  some  designers  as  a  tubular  body  of  air  of  external 
diameter  of  approximately  0*95  times  the  airscrew  diameter,  and 
internal  diameter  of  0*2  times  the  airscrew  diameter.  All 
members  included  within  this  annular  cylinder  are  exposed  to 
the  increased  velocity.  In  the  absence  of  more  definite  results 
bearing  upon  any  particular  design  under  consideration,  the 
curve  shown  in  Fig.  174  can  be  used  to  give  a  rough  estimate 
of  the  increase  in  resistance.  The  value  of  the  Tractive  power 
of  an  airscrew  at  a  given  speed  is  obtained  from  the  equation, 

F        /  V  \2~~| 
Tractive  power  =  k     i  -  (^7-7]       N3D5    Formula  70 

where     N  =  number  of  revolutions  per  second, 
D  =  diameter  of  the  airscrew, 
V  =  forward  speed  of  the  machine, 
p   =  experimental  mean  pitch  of  the  airscrew, 
k  =  constant  whose  value  can  be  determined  experimentally. 


232  AEROPLANE   DESIGN 

If  D  be  the  diameter  of  the  airscrew  used,  then  the  value  of 

the  fraction     r.^.lve  ^°^er  can  be  calculated  for  the  speed  under 
(Diameter)2 

consideration.  The  value  of  the  corresponding  slip  stream  co- 
efficient is  at  once  obtained  from  the  curve  in  Fig.  174,  and  the 
resistance  of  each  component  falling  within  the  slip  stream  must 
be  multiplied  by  this  coefficient. 

Resistance  of  Complete  Machine.  —  The  following  table 
shows  the  estimation  of  the  resistance  of  the  various  parts  of  an 
aeroplane.  The  machine  under  consideration  is  the  B.E.  2, 
total  weight  1650  Ibs.,  with  a  speed  range  of  40-73  m.p.h. 

TABLE  XXXVII.  —  ESTIMATE  OF  BODY  RESISTANCE  OF 
B.E.  2  AT  60  M.P.H. 

STRUTS.  —  8  —  6'  o"  x  ij"  @  -85  Ibs./sq.  ft.         ...     4/2  Ibs. 
4—4'  o"  x  ij"  @       „         ,,  ...     14 

6—3'  o"  x  ij"  {§       „         „  ...     i  -6 

-  7-2 
WIRING.  —  220  feet  cable  @  10  Ibs./sq.  ft.          ...   29-5 

70  feet  12  G.H.T.  wire@  10  Ibs./sq.  ft.     5  '6 
52  strainers,  estimated  ...          ,,.     3*0 

38T 
Rudder  and  elevators         ............     2'o 

Body  with  passenger  and  pilot      .........  40*0 

Axle  @  '85  Ibs./sq.  ft  .............     2*0 

Main  skids  and  axle  mounting,  estimated  ...     ro 

Rear  skid,  estimated         ...         ...          ...         ...       '5 

Wheels  „  ............     3-5 

Wing  skids,  etc.    „  ............   io'o 

-  59'° 


I04'3 
Exposed  to  a  slip  stream  of  25  feet  per  second. 

Body            ..................  40    Ibs. 

4  —  4'  o"  struts         ...         ...         ...         ...         ...  i  '4 

fof3'o"     „            ...............  -8 

50'  o"  cable             .........         *-.t         ...  67 

30'  o"  H.T.  wire     ...          ...          ...         ...         ...  2*4 

Rudder  and  elevator          .....  .         ......  2*0 

Rear  skid     ...         ...         ...         ...         ...         ...  0*5 

Fittings        ...         ...         ...         ...         ...         ...  2*0 


55-8 
Increase   in   resistance   due   to   slip   stream       =  357     357 

Whence  total  resistance  of  machine  =  140-0  Ibs. 


RESISTANCE   AND   STREAMLINING  233 

The  following  data  will  be  found  useful  in  estimating  the 
resistance  of  the  different  members  of  a  machine. 

TABLE  XXXVIII. — RESISTANCE  OF  AEROPLANE  COMPONENTS. 

Resistance  at  100  f.p.s. 
Component.  Normal  area. 

Streamline  struts  ...  1*3  Ibs.  per  sq.  ft. 

Streamline  axle    ..  ...          ...          ...  1*5 

Round  smooth  cable       ...         ...          ...  10 

Stranded  cable     12 

Landing  wheels  ...          ...         ...         ...  4*0 

Fuselage 3-4 

Tail  skid  ...  ...  ...  5-9 

Tail  plane  and  rudder ro 

R.A.F.  wires        3*25 

Wing  skids  5  -o 

Tail  plane  and  aileron  levers      2-5 

Experimental  Measurement  of  the  Resistance  of  Full- 
size  Machines. — Two  methods  have  been  adopted  for  the 
measurement  of  the  resistance  of  actual  machines — 

(i)  By  measuring  the  gliding  angle  of  the  machine  with  the 
engine  switched  off  and  the  propeller  stopped. 

Let  0  =  the  gliding  angle 

then  we  have       tan  0  = Formula  71 

Drag 

In  gliding  flight  the  lift  is  given  by  the  relationship 

Lift  =  W  cos  0  ; . .   Formula  7  2 

so  that  the  drag  is  very  easily  calculated. 

The  value  of  the  drag  thus  obtained  represents  the  total 
resistance  of  the  machine,  that  is  the  wings  and  the  body,  at  the 
speed  of  flight  considered.  The  resistance  of  the  wings  can  be 
calculated  directly  from  the  area  of  the  supporting  surface  and 
the  characteristics  of  the  aerofoil  used  by  applying  Formula  14. 

Corrections  must  be  applied  for  speed  and  scale  effect  and 
also  for  interference  effects.  By  subtracting  the  resulting  re- 
sistance of  the  wings  from  the  total  resistance  obtained 
previously,  the  body  resistance  is  determined,  and  may  be 
compared  with  that  used  in  the  original  estimate  for  the 
purposes  of  preliminary  design.  The  principal  difficulty  en- 
countered in  this  method  results  from  the  very  rapid  change 
which  occurs  in  the  density  of  the  atmosphere  as  the  machine 
descends,  and  which  will  give  rise  to  serious  errors  unless  its 
effect  is  eliminated. 


234  AEROPLANE   DESIGN 

(ii)  By  determining  the  thrust  of  the  airscrew  during  a  series 
of  climbs. 

The  direct  measurement  of  this  thrust  by  means  of  a  thrust 
meter  offers  the  most  convenient  and  accurate  method  of  deter- 
mining the  resistance  of  a  machine,  but  the  difficulty  of  obtaining 
a  reliable  instrument  has  so  far  prevented  the  results  secured  from 
being  of  an  entirely  satisfactory  nature.  It  has  therefore  been 
necessary  to  deduce  the  thrust  from  particulars  of  the  horse- 
power and  the  airscrew  efficiency  of  the  power  unit  employed, 
under  conditions  similar  to  those  encountered  during  the  test. 


f 


FIG.  174. — Slip  Stream  Coefficient. 


Having  obtained  this  information  and  carried  out  the  climbing 
tests,  the  thrust  necessary  to  overcome  the  drag  of  the  machine 
can  be  determined  and  the  body  resistance  deduced,  as  in 
case  (i). 

Skin  Friction. — When  a  fluid  flows  smoothly  over  a  stream- 
line body  such  as  an  efficient  airship  envelope,  or  a  thin  flat 
plate  placed  edgewise  and  assumed  to  have  no  head  resistance, 
a  certain  resistance  is  still  felt  against  the  relative  motion  of  die 
body  and  the  fluid,  which  is  termed  the  skin  or  surface  friction. 
A  thin  film  of  air  covers  the  actual  surface  of  the  body,  being 
entangled  in  the  'roughness'  of  its  outer  layers,  and  imprisoned 
there  by  the  outer  pressure  of  the  air.  The  frictional  force  felt 


RESISTANCE   AND   STREAMLINING  235 

is  partly  due  to  the  continuous  shearing  which  takes  place 
between  this  film  and  the  stratum  of  fluid  adjacent  to  it.  It  is 
therefore  a  function  of  the  viscosity  of  the  fluid.  The  coefficient 
of  viscosity  is  defined  as  the  force  required  to  maintain  a  plate 
of  unit  area  at  unit  velocity  when  it  is  separated  from  another 
plate  by  a  layer  of  fluid  of  unit  depth. 

Stokes  showed  that  so  long  as  the  motion  was  sufficiently 
slow  to  avoid  eddies  the  frictional  resistance  varied  as  the  first 
power  of  the  velocity.  Allen  showed  that  this  stage  was  followed 
by  one  in  which  the  index  of  the  velocity  was  1*5.  In  the  range 
of  velocity  common  in  aeronautical  practice  the  index  appears 
to  lie  between  1-5  and  2.  Lanchester  and  Zahm  further  de- 
veloped the  fundamental  equation,  and  from  the  experiments 
carried  out  by  the  latter,  in  which  the  skin  friction  of  a  large 
number  of  smooth  surfaces  in  a  current  of  air  was  measured,  it 
was  found  that  the  resistance  increased  according  to  the  power 
1*85  of  the  velocity.  Zahm  therefore  developed  the  following 
equation,  connecting  skin  friction  with  the  length  of  the  plane 
and  the  velocity. 

p  oc  L—  °7  V1-85     Formula  73. 

V  =  the  velocity  in  feet  per  second. 
L  =  the  length  of  the  planes  in  feet. 
p  =  the  tangential  force  per  square  foot. 

Lanchester  has  shown  that  to  express  the  resistance  of  a 
plane  in  terms  of  the  linear  size  and  kinematic  viscosity,  the 
relation 

Roc  viLrVr      Formula  74 

Where  R  =  resistance  per  unit  density 

,  .  ...          u       coefficient  of  viscosity 

v  =  kinematic  viscosity  =  "  =  _  __£ 

p  density 

L  =  linear  size 
V  =  velocity 

holds  for  an  incompressible  fluid  when  q  +  r  =  2. 

Expressing  Zahm's  equation  (Formula  73)  in  terms  of  R,  it 
becomes 

R  oc  L1'93  V1'85    Formula  73  (a) 

whereas,  in  order  to  satisfy  Lanchester' s  equation  (Formula  74), 
the  indices  of  L  and  V  should  be  equal. 

Lanchester  has  therefore  adopted  the  following  expression 
for  a  smooth  surface  : — 

R  a  vl  L1 9  V1'9      Formula  74  (a) 


236 


AEROPLANE    DESIGN 


Assuming  that  the  exponent  varies  with  the  nature  of  the 
surface,  as  has  been  found  to  be  the  case  by  actual  experiment, 
Formula  74  (a)  may  be  written  in  the  form 

R  oc  v2-n  Ln  Vn 
Whence  F  =  Rp  =  K,ov2-nLnVn    Formula  75 

For  any  one  surface  it  is  convenient  to  neglect  the  length  and 
embody  its  value  and  the  value  of  p  and  v  in  one  constant, 
when  the  equation  becomes 

F  =  K.Vn        Formula  75  (a) 

The  value  of  K  depends,  of  course,  on  the  units  employed, 
and  both  n  and  K  may  vary  with  the  surface  for  even  so-called 
*  smooth '  surfaces. 

An  exhaustive  series  of  experiments  have  been  carried  out 
at  Washington  to  determine  the  values  of  F,  n,  K  in  the 
simplified  Formula  75  (a)  above.  Plate  glass  was  used  as  a 
standard  surface,  since  it  is  very  smooth,  and  can  be  readily 
duplicated.  The  various  fabrics  were  attached  to  this  surface  by 
a  special  varnish,  to  obtain  as  smooth  a  surface  as  possible  ; 
and  experiments  were  made  at  velocities  of  30  to  70  m.p.h., 
and  the  forces  measured  with  great  accuracy.  The  results 
obtained  are  shown  in  Table  XXXIX.,  where  F  is  in  Ibs. 
per  sq.  ft.,  and  the  resistance  factor  (R.F.)  is  the  ratio  Observed 
resistance  :  Resistance  of  Glass  Plate. 


TABLE  XXXIX. — SKIN  FRICTIONAL  RESISTANCES. 


Nature  of 
surface  exposed. 

PLATE 

GLASS. 

FINE 

LINEN, 

uncoated. 

One  coat 
of 
aero  varnish. 

i 

!  Three  coats 
of 
1  aero  varnish. 

Three  coats  of 
'  aero  varnish 
'   one  coat  of 
.  spar  varnish. 

AEROPLANK 

FABRIC, 

rubber 
surface. 

| 

n  ... 

r8i 

i  -94           1-84 

1-89 

r*4 

I-83 

K  x  IOT  ... 

1  66 

128 

I63 

129 

J53 

165 

m.p.h. 

1 

3°    F 

•0079 

•0095 

'0085 

•0082 

•0081 

•0084 

R.F.  ... 

i*b 

1*205 

I  '08  1 

1*042 

1-031 

1*070 

40   F 

•oi33 

'0161 

•0141 

•0138 

•oi35 

•0142 

R.F.  ... 

I'O 

1*234 

i'o8o 

i"o6o 

1*034 

I-082 

50    F      ... 

•0199 

•0249 

•0218 

•0208 

•0204 

•0215 

R.F.  ... 

I'O 

1*254 

1-098 

1-048 

i    1-028 

1-083 

60    F       ... 

•0276 

•0361 

•0309 

•0295 

•0287 

•0299 

R.F.  ... 

I'O 

I*305 

rn8 

1*067 

1-038 

I  -08  1 

70    F       .. 

•0364 

'0496 

•0424 

•0403 

•0387 

•0393 

R.F.  ... 

I'O 

1*362 

1-162 

1-108 

1 

i  "06  1 

1-079 

RESISTANCE   AND    STREAMLINING  237 

With  the  aid  of  this  table  the  actual  skin  friction  of  an 
aeroplane  wing  surface  can  be  easily  calculated.  It  will  be 
found  that  it  is  a  very  small  quantity.  It  is  only  in  the  case  of 
airships  where  relatively  low  head  resistance  is  combined  with  a 
large  surface  area  that  the  effects  of  skin  friction  are  found  to  be 
considerable. 

Zahm's  experiments  upon  a  series  of  surfaces  of  width  w 
resulted  in  the  following  equation  : — 

F  =  -000007 7 8  wL093  V1'85     Formula  76 

where  F  is  the  friction  in  pounds  at  a  speed  of  V  feet  per  second. 
For  double-sided  planes  this  value  must  be  doubled,  but  when 
estimating  the  surface  friction  of  streamline  shapes  the  single 
value  alone  may  be  employed. 

Zahm's  formula  for  the  skin  friction  of  a  fuselage  is 

F  =  -00000825  A0925  V1'85       Formula  77 

where  A  is  the  superficial  area  in  square  feet,  and  V  the  velocity 
in  feet  per  second. 


CHAPTER  VII. 
DESIGN  OF  THE  FUSELAGE. 

Weights. — Before  proceeding  to  consider  the  general  and 
detail  design  of  the  fuselage,  it  is  necessary  to  examine  more 
closely  the  question  of  the  weights  of  the  various  components  of 
an  aeroplane. 

With  this  object  in  view  Table  XL.  has  been  prepared  from 
an  analysis  of  a  large  number  of  machines  of  various  types,  and 
gives  the  percentage  weights  of  the  different  portions  of  the 
machine  arranged  in  groups.  The  weights  of  the  individual 
members  of  a  group  will,  of  course,  vary  considerably  in 
different  designs. 

TABLE  XL. — PERCENTAGE  WEIGHTS  OF  AEROPLANE  COMPONENTS. 

1.  The  Power  Plant. 

(a)  Engine  ...          ...          ...          ...  2o-o 

(b}  Radiator        2-5 

(c)  Cooling  water  ...          ...         ...         2  -o 

(d)  Tanks  and  pipes       ...         3-0 

(e)  Airscrew        ...         ...          ...         ...         2*5 

30*0 

2.  The  Glider  Portion. 

(a)  Wings             ...  13-0 

(b)  Wing  bracing             ...          ...          ...  3*0 

(c)  Tail  unit        2-0 

(d)  Body...       ....          ...          ...          ...  13*0 

(e)  Chassis  or  undercarriage      4-0 

35'° 

3.  Useful  Load. 

(a)  Fuel  ...          ...          ...          ...          ...        20mo 

(b)  Passengers  and  cargo  14*0 

34-0 

4.  Instruments,  etc.         ...        i'o 

Table  XLI.  gives  particulars  concerning  the  chief  Modern 
Aero  Engines  of  various  types. 


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240  AEROPLANE   DESIGN 

When  considering  the  question  of  design  it  will  be  found 
very  convenient  in  the  preliminary  stages  to  remember  the 
approximate  weights  in  groups  of  items  which  are  associated 
together  in  an  aeroplane.  One  method  is  to  divide  up  the  total 
weight  into  the  three  main  divisions  or  groups  shown  in 
Table  XL.,  namely  : 

1.  The  weight  of  the  power  plant. 

2.  The  weight  of  the  glider  portion. 

3.  The  weight  of  the  useful  load  carried. 

The  proportion  of  these  components  to  the  total  weight  of 
the  machine  is  set  out  in  this  table,  and  the  figures  given  there 
will  serve  as  a  useful  basis  from  which  to  start. 

Another  method  is  to  group  together  the  power  plant,  fuel, 
and  accessories,  and  consider  them  concentrated  at  the  engine 
bearers.  A  second  group  is  made  up  of  the  pilot,  instrument 
board,  control  levers,  and  other  fittings  of  the  cockpit.  A  third 
group  is  formed  by  the  tail  unit,  and  comprises  the  tail  plane, 
elevators,  rudder,  fin,  and  tail  skid.  This  is  a  light  group,  but  as 
it  acts  at  a  long  leverage  from  the  C.G.  it  is  of  importance  for 
balancing  purposes.  In  this  method,  the  chassis  and  wings  being 
close  to  the  C.G.,  may  sometimes  be  neglected  in  obtaining  a 
preliminary  balance,  but  the  effect  of  these  weights  must  not  be 
overlooked  when  the  design  is  finally  considered. 

In  disposing  of  the  weights  it  is  a  good  rule  to  concentrate 
them  as  much  as  possible  in  order  to  reduce  the  moment  of 
inertia  of  the  machine.  Some  latitude  also  must  be  allowed  so 
that  after  the  complete  design  of  the  wings,  chassis,  tail  unit,  etc., 
has  been  got  out,  a  heavy  weight  such  as  the  engine  or  pilot  may 
be  moved  a  short  distance  so  as  to  compensate  for  any  initial 
errors  of  estimation  in  weight  or  leverage.  All  fluctuating  loads 
such  as  fuel,  bombs,  cargo,  should  be  concentrated  as  near  the 
C.G.  as  possible,  so  that  balance  may  be  preserved  after  un- 
loading. 

The  Fuselage.— The  fuselage  has  to  be  strong  enough  to 
stand  up  to  difficult  conditions  in  its  function  as  a  structural 
member.  Its  duties  are — 

1.  To    act  as  a   double   cantilever  in  flight,  supporting  the 
weights  of  the  engine  and  pilot  through  the  agency  of  the  wings. 

2.  To  support  the  same  two  weights  when  the  chassis  strikes 
the  ground  in  a  fairly  bad  landing. 

3.  To  withstand  the  compression  in  the  spars  of  the  wings. 

4.  To  act  as  a  vertically  loaded  beam  when  it  transmits  the 
pitching  moment  due  to  moving  the  elevators,  or  that  due  to  the 
tail  plane  in  a  longitudinal  oscillation. 


Reproduced  by  courtesy  of  Messrs.  Vickers,  Ltd. 

FIG.  178. — Fuselage  of  the  'Vimy'  Bomber. 


Facing  page  240. 


DESIGN    OF   THE    FUSELAGE 


241 


5.  To  act  as  a  horizontally  loaded    beam   when  directional 
moments  are  applied  by  the  rudder  or  the  vertical  fin. 

6.  To  resist  any  torsion  due  to  the  warping  arrangements  or 
the  power  plant. 

Such  a  complexity  of  systems  of  loading  leads  to  a  sym- 
metrical method  of  construction. 


25' 6 


8echon  on  A.O. 


FIG.  175.— Example  of  Wooden  Fuselage. 

In  general  four  main  longerons  run  from  end  to  end  of  the 
fuselage.  Transverse,  horizontal,  and  vertical  struts  divide  the 
main  structure  up  into  a  series  of  panels,  each  of  which  is  cross- 
braced  by  means  of  small  tie-rods  (see  Fig.  176).  For  machines 
fitted  with  stationary  engines  the  vertical  struts  at  the  forward 
end  are  frequently  replaced  by  plywood  formers  cut  to  the 


FIG.  176.— Wooden  Fuselage  with  tubular  Engine  Bearers. 

cross-sectional  shape  of  the  body,  and  lightened  out  wherever 
possible  (see  Fig.  175).  These  formers  transmit  the  direct 
weight  of  the  power  plant  to  the  fuselage.  In  this  manner  a 
very  strong  structure  is  obtained  without  the  addition  of  a 
large  amount  of  weight.  The  longerons  may  be  of  ash,  spruce, 
or  steel  tubes.  The  section  adopted  depends  upon  the  material 
used,  and  also  upon  the  need  for  achieving  minimum  weight. 


242  AEROPLANE    DESIGN 

The  finished  longeron  represents  a  number  of  small  struts, 
joined  together  at  the  ends,  and  bent  to  obtain  a  streamline 
form.  If  lightened  out  the  longeron  must  be  bent  very  care- 
fully in  order  to  prevent  the  introduction  of  initial  strains. 
For  machines  of  about  a  ton  in  weight  the  longerons  may  be 
made  of  wood  cf  i\"  square  section  in  the  important  part> 
tapering  away  at  both  ends.  If  a  single  length  of  good  quality 
is  not  obtainable,  two  pieces  may  be  spliced  together  or  con- 
nected by  a  clip.  Wherever  exposed  to  wearing  conditions  such 
as  foot-rubbing,  engine  heat,  etc.,  they  should  be  sheathed  or 
otherwise  protected.  As  far  as  possible,  holes  in  the  longerons 
should  be  avoided,  in  fact  it  is  good  practice  not  to  pierce  them 
at  all.  If  pierced  to  carry  any  strain-bearing  bolt,  the  bolt 
should  be  supported  externally  by  means  of  flitch  plates.  A 
form  of  clip  can  be  easily  devised  which  satisfies  the  requisite 
conditions  to  take  the  wires  which  radiate  from  the  junction  of 
the  longeron  with  strut,  and  further  keeps  the  strut  in  position. 
From  the  general  arrangement  made  in  the  drawing  office  the 
fuselage  will  usually  be  set  out  full  size  on  a  large  board  in  the 
shops.  The  longerons  may  be  bent  and  the  size  of  the  struts 
cut  off  to  the  very  accurate  shapes  and  dimensions  given  by 
the  latter  drawing,  which  also  supplies  the  local  angles  of  the 
longeron  and  struts. 

The  longerons  are  bound  in  pairs  at  their  rear  ends  to  the 
sternpost,  which  provides  a  strong  fixing  for  the  rudder  and  the 
hinge  spar  for  the  elevators  (the  rear  spar  of  the  tail  plane). 
The  sternpost  may  be  either  of  wood  or  a  steel  tube,  and  may 
also  conveniently  serve  for  the  fixing  of  the  tail  skid  and  of  the 
vertical  fin.  At  their  forward  end  the  longerons  are  bound  to 
the  corners  of  a  square  or  rectangular  plate,  which,  if  the  engine 
is  overhung,  serves  as  an  engine  bearer  plate  (see  Fig.  183),  or 
provides  a  fixing  for  the  extension  shaft  for  the  airscrew. 

The  square  section  given  to  the  fuselage  by  the  longerons 
and  struts  is  far  from  ideal  from  the  standpoint  of  streamlining, 
especially  on  the  top.  The  flat  top  may  be  rounded  off  by 
means  of  fabric  stretched  over  formers.  These  formers  may  be 
built  up  very  lightly  out  of  reinforced  plywood,  lightened  out 
until  there  is  very  little  material  left.  They  may  be  mounted 
over  the  top  struts,  and  connected  together  by  means  of  a  few 
longitudinal  strips.  Fabric  should  be  used  wherever  possible  as 
a  fuselage  covering,  and  three-ply  should  be  avoided  owing  to 
its  much  greater  relative  weight. 

In  this  connection  it  is  important  to  remember  the  results  of 
the  experimental  investigation  into  the  relative  merits  of  the 
square  and  circular  cross-section  aeroplane  bodies  given  in  the 


DESIGN   OF   THE   FUSELAGE  243 

preceding  chapter.  As  will  be  seen  from  Fig.  184,  it  is  possible 
to  build  up  a  fuselage  of  streamline  shape  without  using  a 
square  section  as  the  basis. 

Two  or  three  of  the  top  bracing-panels  will  require  to  be 
omitted  on  account  of: 

1.  The  pilot. 

2.  The  passenger,  if  any. 

3.  The  fuel  tanks. 

4.  Perhaps,  the  engine. 

This  means  collectively  a  serious  weakening,  and  the  panels 
thus  mutilated  should  be  strengthened  by  all  convenient  means. 

Points  of  attachment  of  heavy  weights,  such  as  pilot,  pas- 
senger, tanks,  etc.,  should  be  made  to  the  longerons  at  the  cross 
panels.  This  principle  must  be  the  chief  guide  in  setting  out  the 
fuselage,  and  it  should  be  remembered  that  bending  moments  are 
to  be  avoided  as  far  as  possible  in  any  member  of  the  body. 
Further,  where  a  compressive  force,  as  from  the  wings,  comes 
on  the  fuselage  a  specially  strong  strut  should  be  arranged  to 
take  the  strain  directly,  and,  where  a  tension  may  be  applied,  a 
special  tension  member  should  be  introduced.  The  sizes  of  these 
members  are  calculated  in  the  usual  manner. 

The  general  arrangement  of  the  fuselage  may  be  conveniently 
set  out  by  drawing  a  section  longitudinally,  and  then  making 
drawings  of  each  cross  panel.  The  formers,  wherever  used, 
should  be  included  in  the  transverse  sections. 

It  is  useful  to  have  cardboard  models  of  a  pilot  to  the  scales 
most  generally  used  in  the  office,  as  there  is  frequently  a  question 
as  to  clearance  between  some  portion  of  the  pilot's  body  and 
the  various  fittings  in  the  cockpit. 

The  engine  is  the  limiting  factor  in  considering  the  design  of 
the  fuselage  aerodynamically.  If  a  radial  engine  is  used  it  may 
be  hung  on  the  nose  of  the  fuselage  and  partially  protected  by 
a  cowl,  or  it  may  be  totally  enclosed  some  way  back.  The 
second  method  gives  much  greater  scope  with  regard  to  the 
streamlining  of  the  fuselage,  although  it  is  impossible — owing  to 
considerations  of  balance — to  get  the  Engine  back  far  enough. 
It  has  the  great  drawback,  however,  that  it  greatly  increases 
the  weight  owing  to  the  extension  of  the  airscrew  shafting, 
bearings  for  same,  and  extra  engine-bearing  plates  of  large  size. 
It  is  further  liable  to  accidental  fires.  In  the  case  of  the 
heavier  type  of  the  fixed  cylinder  engine  its^  greater  weight 
will  necessitate  a  less  forward  position,  leading  to  greater  ease 
in  aerodynamic  design.  On  account,  however,  of  the  shaft,  and 
consequently  the  airscrew,  being  at  the  bottom  of  the  engine 
instead  of  in  the  middle,  it  will  be  difficult  to  totally  enclose  the 


244  AEROPLANE   DESIGN 

engine  without  unduly  increasing  the  height  of  the  chassis,  still 
keeping  to  the  minimum  section  of  body.  The  cylinder  heads 
are  often  left  exposed  in  this  type  of  engine  and  may  spoil 
an  otherwise  good  design,  more  especially  if  the  heads  happen 
to  be  placed  in  the  airscrew  slip-stream.  In  important  cases, 
and  in  fact  whenever  possible,  different  designs  should  be 
tested  in  the  wind  tunnel  and  compared  from  the  point  of  view 
of  weight  and  cheapness  to  manufacture.  As  we  have  pre- 
viously seen,  a  small  saving  in  head  resistance  is  likely  to  be  of 
great  importance  in  high-class  work.  When  considering  the 
question  of  skin  friction  of  a  fuselage,  Zahm's  formula  may  be 
used,  namely  : 

Skin-friction  =  '00000825  A°'925  y1'85 
where  A  is  the  superficial  area  in  square  feet 
V  is  the  velocity  in  feet  per  second. 

Assuming  ordinary  dimensions,  it  will  be  seen  on  applying 
this  formula  that  air  friction  accounts  for  about  half  of  the  total 
resistance  of  a  good  fuselage  shape.  The  total  head  resistance 
of  the  fuselage  will  then  vary  as  a  power  of  the  velocity  between 
1*85  and  2.  Wind-tunnel  tests  would  be  useful  to  a  designer 
in  assessing  the  true  value  of  this  index  for  a  particular  case. 

The  importance  of  keeping  the  maximum  cross-sectional  area 
low  should  not  be  lost  sight  of.  It  is  frequently  argued,  and  it 
is  often  true,  that  it  is  better  to  waste  space  by  increasing 
the  maximum  cross  dimensions  of  the  fuselage,  if  by  so  doing 
the  '  lines '  of  the  fuselage  may  be  improved.  The  principle 
is  a  sound  one  within  certain  prescribed  limits,  but  it  is  easy  for 
an  enthusiast  in  streamlining  to  increase  the  maximum  section 
of  the  fuselage  by  2"  to  3"  all  round,  thus  increasing  the 
maximum  cross-sectional  area  by  some  30%.  This  means  that 
the  coefficient  of  head  resistance  of  the  thicker  shape  would  have 
to  be  improved  by  the  same  amount  (30%)  in  order  that  the  en- 
larged body  should  have  as  small  a  resistance  as  the  original 
body,  and  more  than  this  amount  if  improvement  is  to  be 
attained.  The  size,  therefore,  should  be  kept  as  small  as  possible 
consistent  with  housing  the  engine  and  pilot  and  without  unduly 
exposing  parts  of  either  to  the  wind.  This  last  consideration 
will  limit  the  size  of  the  cockpit  opening  and  lead  to  a  small 
shield,  a  few  inches  only  in  height,  being  placed  on  the  forward 
half  of  the  cockpit  opening  in  order  to  spill  the  air  over  the 
opening. 

It  is  interesting  to  note  in  this  connection  that  totally  en- 
closing the  fuselage  cockpits  results  in  a  greatly  reduced 
resistance.  For  example,  the  Vickers'  Commercial  machine, 


DESIGN    OF   THE    FUSELAGE  245 

the  fuselage  of  which  will  be  shown  later  in'this  chapter,  is  10% 
faster  than  its  prototype,  the  Vickers'  Vimy  Bomber.  This  and 
other  types  of  fuselage  used  in  modern  practice  are  shown  in 
Figs.  175-184. 

In  the  fuselage  shown  in  Fig.  175  it  will  be  observed  that 
the  longerons  are  supported  in  their  correct  position  by  means 
of  three-ply  formers  in  the  front  portion  and  by  means  of  struts 
and  wires  in  the  rear  portion. 

An  excellent  type  of  fuselage  is  that  of  the  Bristol  Fighter, 
'which  is  shown  in  Fig.  176.  The  front  portion,  comprising  the 
engine-bearers,  is  composed  of  tubular  steel,  while  th~  remain- 
ing portion  of  the  structure  is  built  up  of  wood  braced  together 
with  small  tie-rods.  The  depth  of  the  beam  increases  towards 
the  centre  of  the  machine  and  thereby  helps  to  keep  the  bending 
stresses  low  throughout. 

In  order  to  afford  a  comparison  between  the  fuselages  of  two 


FIG.  177. — Fuselage  of  Handley-Page  (0-400)  Machine. 


machines  which  are  being  largely  adopted  for  commercial  work, 
and  to  illustrate  the  different  methods  employed  in  practice  in 
building  large  fuselages,  the  fuselages  of  the  Handley-Page  and 
the  Vickers'  machine  are  shown  in  Figs.  177  and  178. 

As  will  be  seen,  the  Handley-Page  follows  the  construction 
of  the  types  already  illustrated,  while  the  Vickers'  machine 
'  exhibits  a  totally  different  type  of  construction.  As  adapted  to 
commercial  uses  the  passenger  cabin  of  the  latter  machine  is  of 
considerable  interest.  It  may  be  mentioned  in  passing  that  the 
sole  modification  of  the  well-known  war  machine  of  the  Vickers 
Company,  the  Vimy  Bomber,  for  commercial  purposes,  lies  in 
the  use  of  a  different  fuselage.  As  will  be  seen  from  Fig.  179, 
the  shell  of  the  cabin  is  built  up  of  oval  wooden  rings  of 
three-ply  box  section,  the  formers  being  shown  in  the  back- 
ground of  Fig.  179.  The  cover  of  the  cabin  is  made  according 
to  the  '  Consuta '  patent  of  Saunders,  of  Cowes,  and  is  con- 
structed of  thin  layers  of  selected  wood,  the  grain  being  placed 
diagonally,  and  then  glued  and  sewn  together,  the  rows  of  stitch- 
ing running  in  parallel  lines  about  ij"  apart.  The  strength  of 
this  material  is  very  great,  giving  a  high  factor  of  safety  to  the 


246 


AEROPLANE   DESIGN 


cabin,  and  enabling  all  cross-bracing  wires  to  be  dispensed 
with  in  the  interior  of  the  cabin,  as  shown  in  Fig.  180.  An 
exterior  view  of  the  completed  cabin  is  shown  in  Fig.  18 1. 

Fig.  182  illustrates  the  fuselage  of  the  Fokker  Biplane.  It 
will  be  seen  that  it  is  built  up  of  thin  steel  tubes  which  are 
welded  together.  The  longerons  are  fixed  relatively  to  one 
another  by  means  of  cross  struts  butt-welded  to  the  longerons 
and  by  means  of  bracing  wires.  This  method  of  construction 
has  not  proved  very  successful  up  to  the  present,  mainly  on 
account  of  the  difficulties  of  welding  and  brazing,  and  it  is  found 


FIG.  182. — Example  of  Steel  Fuselage. 

that  for  a  given  weight  a  wooden  fuselage  is  stronger.  It  is 
more  probable  that  the  steel  fuselage  of  the  future  will  be 
constructed  by  the  methods  usually  adopted  in  other  engineer- 
ing structures,  namely,  by  means  of  steel  channels  and  angle 
irons.  By. this  means  the  expensive  steel  sockets  and  fittings 
necessary  at  the  joints  of  a  wooden  structure  can  be  avoided, 
while  the  work  involved  in  pressing  out  a  steel  channel  or  angle 
iron  to  the  desired  shape  is  very  much  less  than  the  process  of 
producing  such  a  member  in  wood.  Moreover,  it  can  readily 
be  lightened  when  necessary  and  desirable  by  punching  holes 
in  it.  The  Sturtevant  Company  of  America  have  already  pro- 
duced fuselages  upon  these  lines,  and  apparently  with  some 
success.  One  type  of  their  large  battle-planes  is  fitted  with  a 
steel  fuselage  which,  complete  with  steel  engine-bearers  and 


DESIGN    OF   THE    FUSELAGE 


247 


bracing,  weighs  only  165  Ibs.  It  is  estimated  that  a  wooden 
structure  of  equal  strength  would  weigh  over  200  Ibs.  The 
Sturtevant  fuselage  has  been  found  quite  satisfactory  in  a  series 
of  prolonged  tests,  and  there  is  little  doubt  that  in  process  of 
time  the  use  of  steel  or  light  alloys  in  this  direction  will  be 
very  greatly  extended. 

Fig.  183  illustrates  the  fuselage  of  a  small  scout  machine, 
namely,  the  Sopwith  Camel.  It  follows  the  usual  girder  type  of 
construction.  The  longerons  at  the  forward  end  fit  into  a 
pressed  steel  engine  bearer  which  carries  the  rotating  engine 
with  which  this  machine  is  fitted.  The  engine  cowl  is  attached 
to  the  circular  tube  seen  at  the  fore  end. 

Fig.  184  illustrates  the  fuselage  of  the  German  Pfalz,  and 
gives  an  excellent  idea  of  the  body  formers  and  the  position 
of  the  longerons  for  obtaining  a  good  streamline  shape. 


FIG.  183. 


Stressing  the  Fuselage. — The  method  of  stressing  the 
fuselage  will  now  be  briefly  considered.  For  the  general  type 
of  fuselage  structure  such  as  is  shown  in  Figs.  176,  177,  178,  182, 
183,  the  determination  of  the  stresses  in  the  various  members  is 
not  a  difficult  matter  once  the  external  loads  upon  the  structure 
have  been  estimated.  It  is  customary  to  stress  the  rear  portion 
of  the  fuselage  for  the  tail  load  alone,  this  being  considered  as 
an  isolated  load  acting  at  the  point  of  attachment  of  the  tail 
plane  to  the  fuselage.  The  tail  plane  may  be  subject  either  to 
lift  or  to  down  load,  thus  causing  the  fuselage  members  to 
be  subject  to  reversed  stresses.  The  usual  method  of 
designing  the  tail  plane  is  to  assume  it  to  be  subject 
to  a  uniform  load  per  square  foot  of  area.  This  having 
been  decided  upon,  the  total  load  applied  by  the  wind  forces 
through  the  tail  plane  upon  the  fuselage  is  easily  determined. 
It  is  common  practice  to  assume  a  loading  of  from  15  to  25  Ibs. 
per  square  foot  of  tail  surface,  either  up  or  down  forces,  the 
larger  figure  being  adopted  where  a  high  factor  of  safety  is 
desired.  The  principal  load  upon  the  front  portion  of  the 


248 


AEROPLANE    DESIGN 


FIG.  179. 


FIG.  180. 


FIG.  181, 


Reproduced  by  courtesy  of  Messrs.  Vickers,  L,td. 

Construction  of  Passenger  Cabin  for  Vickers'  Commercial  Machine. 

Facing  page  248. 


DESIGN   OF   THE    FUSELAGE 


249 


fuselage  is  that  of  the  power  plant,  which  includes  engine, 
radiator,  fuel,  tanks,  etc.  Having  decided  upon  the  position  in 
which  these  items  are  to  be  fixed,  the  structure  can  be  stressed 
in  the  usual  manner.  An  example  of  stressing  the  fuselage  is 
shown  in  Fig.  185.  It  has  been  assumed  that  the  machine  is 
fitted  with  a  tail  plane  of  35  square  feet  in  area,  and  of  weight 
40  Ibs.  The  maximum  down  load  on  the  tail  plane  is  to  be 
25  Ibs.  per  square  foot.  The  total  load  acting  at  the  rear  end  of 
the  fuselage  is  therefore  35  x  25  +  40  =  915  Ibs.  This  is  dis- 
tributed equally  on  each  side  of  the  structure,  making  458  Ibs. 
to  be  applied  on  each  girder.  A  side  elevation  of  the  fuselage 


458 


FIG.  185. — Stress  Diagram  for  Fuselage. 

is  next  drawn  out  as  in  Fig.  185  (a),  and  the  stress  diagram 
for  the  rear  section  then  follows,  as  shown  in  Fig.  185  (£). 

From  the  table  of  stresses  prepared  from  this  diagram  the 
necessary  sizes  of  the  members  in  the  rear  portion  of  the  fuselage 
can  be  determined.  Referring  first  to  the  longitudinal  members, 
it  will  be  found  that  they  must  be  designed  for  compressive  loads. 
For  this  purpose  the  Rankine  Strut  formula  may  be  used,  the 
constants  being  taken  from  Fig.  89. 

In  using  Rankine's  formula,  it  generally  happens  that  the 
area  chosen  gives  a  crippling  load  much  above  or  much  below 
the  value  required.  To  obtain  a  close  approximation,  several 
values  have  to  be  tried,  though  other  considerations  frequently 
intervene  to  fix  the  sizes. 


250  AEROPLANE   DESIGN 

The  vertical  struts  are  generally  of  the  same  thickness  as  the 
longerons  at  their  junction  to  the  latter,  but  may  with  advantage 
be  spindled  out  intermediately.  A  section  such  as  that  shown 
in  Fig.  185  (d)  will  be  suitable.  The  sizes  should  be  checked 
by  means  of  Rankine's  formula  modified  as  in  the  case  of  the 
longerons  ;  in  fact,  it  is  a  good  plan  if  one  is  engaged  on  much 
strut  work  to  graph  this  formula  for  various  standard  sections, 
so  that  much  tedious  computation  is  avoided. 

The  front  portion  of  the  fuselage  may  next  be  considered. 
The  principal  load  occurring  on  it  is  the  engine  and  radiator. 
For  this  design  the  weight  is  about  800  Ibs.  Half  of  this  load 
•  is  carried  by  each  side  and  in  turn  distributed  over  the  struts 
which  carry  the  engine  bearers.  The  stress  diagram  can  then 
be  drawn  as  in  Fig.  185  (c).  It  will  be  seen  that  the  loads  are 
so  light  that  the  longerons  will  take  them  comfortably,  and  in 
practice  the  nose  portion  is  very  rarely  stressed.  It  must  be 
remembered,  however,  that  they  have  also  to  take  the  vibration 
due  to  the  engine,  so  that  it  is  inadvisable  to  reduce  them  in 
size,  as  the  structure  might  shake  to  pieces. 

The  fuselage  shown  has  three-ply  wood  J"  thick  over  the 
entire  front  of  the  structure. 

There  remains  to  be  considered  the  stresses  in  the  centre 
portion  of  the  body  when  the  machine  lands.  Half  the  maximum 
landing  shock  will  be  taken  by  each  landing  wheel.  This  force 
may  be  resolved  into  two  components  along  the  under-carriage 
struts,  and  these  components  will  set  up  a  direct  compression  in 
the  vertical  struts  of  the  fuselage,  and  place  the  portion  of  the 
longeron  between  them  in  tension.  When  designing  this  por- 
tion of  the  fuselage,  the  effect  of  this  tension  must  be  considered, 
and  care  taken  to  see  that  the  longeron  is  sufficiently  strong 
for  this  purpose.  Where  possible  it  should  always  be  arranged 
that  the  principal  loads  act  upon  the  vertical  struts  so  that  the 
longerons  are  not  called  upon  to  act  as  beams,  but  are  only 
subject  to  direct  tensile  or  compressive  stresses. 

Design  of  the  Engine  Mountings. — Before  commencing 
to  examine  the  various  types  of  engine  mountings,  a  few  notes 
as  to  the  problems  involved  will  be  useful.  We  shall  first 
consider  the  stationary  vertical  type  of  engine,  this  being 
perhaps  in  most  general  use.  The  engine  itself  consists  of  4,  6, 
or  sometimes  8  cylinders  placed  one  behind  the  other  in  a 
straight  line  on  top  of  a  common  crankcase.  This  arrangement 
of  cylinders  makes  for  a  somewhat  long  engine  bed,  which  must 
be  very  rigid  if  misalignment  is  to  be  avoided.  Some  types  of 
engine  have  been  supported  by  transverse  members  running 


DESIGN   OF   THE   FUSELAGE  251 

through  the  crankcase  from  side  to  side,  but  in  the  majority  of 
cases  the  two  sides  of  the  crankcase  are  provided  with  horizontal 
flanges  running  the  whole  length  of  the  engine,  or  else  with 
brackets  projecting  out  from  the  sides  at  intervals,  designed  to 
be  bolted  on  to  longitudinal  engine  bearers  resting  on  the  body 
structure  of  the  aeroplane. 

The  problem  confronting  the  designer  is  to  provide  a  structure 
which,  while  rigid  enough  to  ensure  that  the  engine  itself  is  not 
subjected  to  any  bending  stresses,  is  yet  sufficiently  flexible  to 
transmit  the  vibration  of  the  engine  to  the  mounting,  and  yet 
damp  out  these  vibrations  before  they  reach  the  structure  of  the 
aeroplane  '  fuselage '  proper. 

In  this  connection  it  should  be  remembered  that  apart  from 
such  minor  considerations  as  vibration,  which  should  be  reduced 
to  a  minimum  in  a  modern  engine,  there  are  two  main  loads  to 
be  considered.  One  is  the  weight  of  the  engine,  which  is  always 
acting,  while  the  other  is  the  thrust  or  pull  of  the  airscrew  acting 
only  when  the  engine  is  running,  and  varying  from  a  maximum 
when  the  engine  is  going  'all-out'  to  a  minimum  when  it  is 
throttled  right  down.  There  is  also  the  reverse  thrust  when  the 
machine  is  diving  and  the  air  pressure  on  the  back  of  the  screw 
is  driving  the  engine. 

It  will  thus  be  seen  that  these  two  main  loads  give  one  ver- 
tical component  and  one  horizontal  component.  Neither  is 
constant,  for  during  a  vertical  nose-dive  with  engine  running, 
the  weight  of  the  engine  is  acting  along  the  same  line  as  the 
thrust,  both  tending  to  pull  the  engine  out  of  the  fuselage  in  a 
forward  direction.  Moreover,  as  we  have  already  seen,  the 
horizontal  component  varies  both  in  magnitude  and  direction. 
In  general,  however,  we  may  consider  the  two  components  as 
being  vertical  and  horizontal  respectively. 

In  normal  flight  the  resultant  of  these  two  components  will 
have  a  forward  inclination  of  approximately  45°.  This  may  be 
illustrated  as  follows  : — Consider  an  engine  of  the  average  ver- 
tical type  weighing,  say,  5  Ibs.  per  h.p. — this  is  somewhat  high, 
but  will  illustrate  the  point — and  the  thrust  obtained  with  an 
airscrew  of  average  efficiency  as  5  Ibs.  per  h.p.,  it  will  be  seen 
that  the  vertical  and  horizontal  components  are  approximately 
equal  in  magnitude,  and  their  resultant  will  therefore  have  an 
inclination  of  approximately  45°. 

For  a  100  h.p.  engine  weighing  5  Ibs.  per  h.p.  and  giving  a 
thrust  of  5  Ibs.  per  h.p.,  the  resultant  will  therefore  be  about 
.700  Ibs.  acting  at  an  angle  of  45°.  During  a  vertical  dive  the  weight 
component  will  be  parallel  to  the  thrust  component,  and  hence 
for  the  same  engine  the  pull  tending  to  tear  it  out  of  the  fuselage 


252 


AEROPLANE    DESIGN 


will  be  about  1000  Ibs.,  that  is,  twice  the  weight  of  the  engine. 
When  diving  with  engine  off',  the  thrust  will  operate  against  the 
weight  and  thus  reduce  the  forward  pull  on  the  engine  bearers. 

There  are  several  different  ways  in  use  for  transmitting  the 
load  from  the  longitudinal  bearers  to  the  body  structure  proper. 
In  some  machines  the  engine  is  supported  at  each  end  only, 
while  others  have  three  or  four  points  of  support.  The  question 


Reproduced  by  courtesy  of  '  Flight. ' 

FIG.  186. 


FIG.  187. 


of  the  number  of  supports  to  employ  depends  largely  upon  the 
size  of  the  engine. 

Wood  is  the  most  common  material  used  for  the  direct 
support  of  the  engine,  this  being  largely  on  account  of  its 
greater  resiliency,  which  acts  to  a  certain  extent  as  a  'shock 
absorber,'  and  thereby  lessens  the  vibration. 

We  shall  now  consider  several  practical  examples  of  engine 


FIG.    188. 

mountings.  The  arrangement  of  engine  bearers  on  an  Albatross 
biplane  is  shown  in  Fig.  186.  The  two  longitudinal  members 
are  of  ash,  and  are  supported  by  transverse  members  connecting 
them  to  the  upper  and  lower  longitudinals  of  the  fuselage.  The 
front  transverse  member  takes  the  form  of  a  pressed  steel  frame 
lightened  in  places  and  joining  a  capping  plate  over  the  ends 
of  the  four  longitudinals  which  converge  somewhat  at  this  point. 
The  next  support  is  joined  by  a  ply-wood  member  20  mms. 
thick,  cut  out  in  places  for  lightening  purposes.  From  the 


DESIGN   OF   THE    FUSELAGE  253 

point  on  the  lower  longitudinals  where  the  front  landing  chassis 
struts  are  attached,  two  supporting  transverse  members  radiate. 
One  of  these,  which  is  of  the  same  thickness  and  general  con- 
struction as  the  preceding  one,  slopes  forward,  while  the  other, 
supporting  the  rear  end  of  the  engine,  has  a  backward  slope. 
The  thickness  of  the  latter  member  is  25  mms. 

In  the  Curtiss  biplane  the  engine  is  supported  by  two  trans- 
verse members  only,  and  for  the  comparatively  light  engine 
employed  this  is  quite  adequate  (see  Fig.  187).  The  front 
support  takes  the  form  of  a  steel  plate  lightened  out,  and  with 
the  edges  turned  in  to  stiffen  the  plate  against  buckling.  At 
the  rear  the  engine  bearers  rest  on  a  transverse  member,  which 
is  in  turn  secured  to  the  upright  body  struts.  Each  bearer  is 
clamped  to  the  transverse  beam  by  two  bolts  as  shown  in 
sketch. 

As  the  engine  overhangs  the  front  chassis  struts,  the  bracing 


Reproduced  by  courtesy  of  'Flight.' 

FIG.  189. 

of  the  sides  of  the  fuselage  has  to  be  sufficiently  strong  to  with- 
. stand  landing  shocks,  and  for  this  reason  the  wiring  of  the  front 
bays  is  in  duplicate. 

An  excellent  type  of  engine  bearer  for  either  vertical  or 
V-type  stationary  engines  is  shown  in  Fig.  188. 

Another  interesting  type  of  mounting  is  that  fitted  to  the  all- 
steel  Sturtevant  biplane  (Fig.  189).  Here  it  will  be  observed 
that  the  engine  bearers  are  of  ash,  supported  by  members  of 
channel  steel.  Four  supports  carry  each  bearer,  three  running 
to  the  point  where  the  under-carriage  struts  are  attached  to  the 
fuselage  longerons.  In  addition  to  their  forward  slope  the 
channel  steel  supports  are  inclined  inwards,  thus  effecting  a  very 
rigid  bracing  of  the  engine  in  every  direction. 

An  additional  consideration  in  the  mounting  of  air-cooled 
stationary  engines  is  that  of  providing  the  necessary  cooling 
effect.  It  seems  probable  that  ultimately  the  air-cooled  engine 
will,  on  account  of  the  large  reduction  in  weight  resulting  from 
the  absence  of  radiators  and  water  tanks,  supersede  the  water- 
cooled  type,  so  that,  although  the  water-cooled  engine  is  now 


254  AEROPLANE    DESIGN 

used  almost  universally,  it  is  well  to  keep  in  sight  the  ad- 
vantages to  be  derived  from  an  efficient  air-cooled  engine.  It 
will  be  realised  that  since  the  cylinders  are  usually  placed  in 
two  rows  of  4,  6,  or  8  each,  according  to  size  of  engine,  the 
front  cylinders  will  have  a  shielding  effect  upon  the  rear  ones, 
which,  as  a  consequence,  will  be  insufficiently  cooled,  and  this 
will  lead  to  trouble.  The  method  usually  adopted  in  the  tractor 
type  of  machine  is  to  direct  the  air  by  means  of  deflector 
plates  so  that  it  enters  the  space  between  the  two  rows  of 
cylinders  from  the  front,  is  prevented  by  a  vertical  partition 
from  escaping  at  the  rear,  and  is  thus  forced  by  the  pressure 
of  the  incoming  air  out  through  the  spaces  between  the  adjacent 
cylinders. 

In  the  pusher  type  of  machine  the  difficulty  was  overcome  by 
mounting  a  large  enclosed  centrifugal  fan  on  the  front  end  of 
the  crankshaft.  The  space  between  the  cylinders  was  covered 
by  an  arched  roof  of  aluminium  running  from  the  tops  of  the 
cylinders  on  one  side  to  the  tops  of  the  cylinders  on  the  other. 
The  Vee  between  the  last  two  cylinders  was  covered  by  a  vertical 
aluminium  plate.  When  the  fan  sucked  the  air  into  the  space 
between  the  rows  of  cylinders  the  only  escape  for  the  air  was 
the  small  spaces  between  adjoining  cylinders,  which  were  thus 
cooled  on  three  sides — the  inner  side,  the  front,  and  the  back — 
while  the  outer  sides  of  the  cylinders  were  cooled  by  the  air 
current  due  to  the  forward  speed  of  the  machine.  This  method 
proved  very  satisfactory  for  the  '  pusher  '  machine. 

Considerable  diversity  of  practice  occurs  with  the  mounting 
of  rotary  engines,  but  the  different  methods  may  be  divided  into 
two  categories:  (I),  those  in  which  the  motor  is  supported  be- 
tween two  plates ;  (2),  those  in  which  the  motor  itself  is  over- 
hung. This  latter  method  allows  of  ready  accessibility  of  the 
engine  when  repairs  are  necessary,  but  is  probably  slightly 
heavier  than  the  double  bearer  mounting,  owing  to  the  necessity 
of  using  a  thicker  gauge  material. 

Fig.  190  illustrates  an  example  of  the  first  method.  The 
plates  are  pressed  from  sheet  steel  and  all  the  edges  are  flanged 
in  order  to  prevent  buckling.  The  front  plate  takes  the  ball  race 
through  which  the  airscrew  shaft  runs,  while  to  the  rear  bearer 
is  bolted  the  back  plate  of  the  engine.  Great  care  is  necessary 
in  cutting  out  the  lightening  holes,  and  these  should  be  such  as 
not  to  materially  diminish  the  strength  of  the  plates.  The 
general  arrangement  of  the  front  part  of  the  fuselage  will  be  clear 
from  the  drawing. 

An  example  of  the  overhung  method  is  shown  in  Fig.  191. 
In  this  case  the  back  plate  of  the  engine  is  attached  to  the 


DESIGN    OF   THE    FUSELAGE 


255 


front  of  the  front  engine  bearer,  while  the  rear  bearer  acts  as  a 
support  to  an  extension  shaft  which  passes  through  both  bearers. 
The  plates  are  pressed  out  of  sheet  steel  either  by  machine  or 
hand,  and  care  is  necessary  to  ensure  that  they  are  attached  to 
the  longerons  in  a  suitable  manner. 

A  problem  of  considerable  importance  in  connection  with 
the  housing  of  rotary  engines  is  that  of  obtaining  sufficient 
cooling  effect  with  a  minimum  of  head  resistance.  The  method 
generally  adopted  is  to  fit  a  cowl  or  sheet  metal  shield  over 
the  engine.  In  the  majority  of  machines  only  the  upper  part  of 
the  engine  is  covered. 


Reproduced  by 
courtesy  of ' ''Flight 


FIG.  190. 


FIG.  191, 


Radiators. — With  the  increasing  demand  for  larger  engine 
power  and  the  difficulties  encountered  in  air-cooling  methods 
the  question  of  water-cooling  has  become  of  great  importance,, 
and  it  will  be  useful  to  consider  this  subject  briefly.  The 
type  of  radiator  in  most  general  use  for  aero  engines  has  de- 
veloped principally  from  the  motor-car  radiator.  According 
to  the  present  practice  there  can  be  but  little  doubt  that  the 
honeycomb  type  of  radiator  holds  the  lead,  whether  it  is 
mounted  in  the  fuselage  or  elsewhere.  In  the  absence  of  wind- 
tunnel  tests  it  is  difficult  to  say  whether  the  square  tube,  round 
tube,  or  other  formations  are  best  as  regards  the  ratio  of  cooling 
capacity  to  wind  resistance. 

•  COOLING  AREA  OF  RADIATORS. — The  'following  method 
was  adopted  by  Lanchester  in  order  to  determine  the  area  of 
cooling  surface  required.  The  heat  units  disposed  of  per  square 
foot  of  single  service  may  be  expressed  by  the  equation  : 

„        o-24ECPVT 

H  =  -  Formula  78 

2 

where  E  =  double  surface  coefficient  of  skin  friction  =  -008 

C  =  normal  plane  resistance  coefficient  =    *6 

V  =  velocity  of  air  stream, 

T  =  temperature  difference,  say  120°  Fahr. 

P  =  -078 


AEROPLANE    DESIGN 

Taking  velocity  of  the  air  stream  equal  to  50  ft/sec,  then  the 
heat  units  disposed  of  per  sq.  ft.  of  surface 

•24  x  -008  x  -6  x  '078  x  50  x  120  ,,  ,      TT  TT 

-  Fahr.  H.U.  per  sec. 

=  -27 

and  the  horse-power  equivalent  =  — ~- — - —    =  '4  nearly 

(Note  that  780  is  the  work  equivalent  of  i  Fahr.  Heat  Unit.  Hence 
under  the  above  conditions,  and  for  a  velocity  of  50  ft.  /sec.,  about  2^ 
square  feet  of  radiator  surface  are  required  per  h.p.) 

The  above  values  for  the  coefficients  were  obtained  from 
experiments  carried  out  on  a  motor-car  radiator,  and  the  results 
were  in  good  agreement  with  general  practice. 


FIG.  192. 

The  increased  speed  with  which  the  radiator  on  an  aeroplane 
meets  the  air  stream  will  bring  down  the  cooling  surface  area 
inversely  as  the  speed,  and  the  above  formula  may  be  used  to 
determine  the  necessary  radiator  surface  required. 

It  is  found  practically  that  if  the  radiator  is  placed  imme- 
diately behind  the  airscrews,  about  1*6  to  r8  square  feet  of  area 
per  100  h.p.  is  required ;  whereas,  if  it  is  placed  so  that  it  gets 
the  full  effect  of  the  slip  stream,  about  I  square  foot  of  area  per 
100  h.p.  is  necessary.  In  the  Airco  9,  the  radiator  is  arranged 
in  the  floor  of  the  front  portion  of  the  fuselage,  so  that  a  greater 
or  less  portion  can  be  exposed  at  will,  according  to  the  pre- 
vailing conditions. 

A  form  of  honeycomb  radiator  which  is  being  largely  used 
on  modern  aeroplanes  is  shown  in  Fig.  192.  The  water  spaces 
consist  of  a  series  of  semi-circles  and  quarter-circles.  Each  air 


DESIGN    OF   THE    FUSELAGE  257 

channel  is  formed  of  a  strip  of  brass,  the  ends  of  which  are 
folded  over  and  joined  by  a  machine.  The  strips  are  then 
placed  in  a  press  and  given  their  correct  shape,  after  which  the 
honeycomb  is  completed  by  soldering  the  ends  of  the  adjoining 
strips  together.  A  point  in  favour  of  this  type  of  radiator  is  that 
it  can  be  built  up  in  units  or  sections  of  almost  any  size. 
Further,  repairs  can  be  quickly  and  cheaply  effected,  a  damaged 
section  being  simply  removed  and  a  new  one  substituted. 

The  Denny  Jointless  Honeycomb  Radiator  is  constructed 
by  the  electro-deposition  of  pure  copper,  so  that  the  re- 
sultant radiator  is  all  in  one  piece,  thus  eliminating  soldered 
joints. 

A  useful  system  which  has  recently  been  taken  up  is  one  in 
which  a  radiator  is  built  up  of  a  number  of  standardised  units 
in  such  a  manner  that  for  a  given  engine  a  certain  number  of 
units  are  employed.  If  the  same  engine  is  used  on  a  faster 
machine  fewer  units  are  employed  ;  if  on  a  slower  one,  more 
units.  The  advantage  of  such  a  system  is  that  instead  of  a 
different  size  and  shape  of  radiator  varying  for  each  type  of 
machine,  and  even  in  the  same  machine  according  to  the 
engine  fitted,  the  standard  unit  can  be  turned  out  in  quantities 
irrespective  of  the  machine  to  which  it  is  to  be  fitted.  This 
naturally  leads  to  rapidity  and  economy  of  production. 

Some  German  machines  have  been  fitted  with  radiators  in 
the  top  centre  section  of  the  main  planes,  but  it  is  very  doubtful 
whether  the  increased  complications  of  such  a  system  are  worth 
while,  either  from  a  practical  or  an  aerodynamical  standpoint. 

Gyroscopic  Action  of  a  Rotary  Engine  and  the  Air- 
screw.— Before  concluding  this  chapter  it  is  desirable  to 
say  a  few  words  upon  this  subject,  since  the  effect  is  to  pro- 
duce a  sideways  twist  upon  the  engine-bearer  end  of  the 
fuselage.  From  the  practical  point  of  view  this  twist  can  be 
easily  provided  for,  and  from  the  pilot's  point  of  view  it  is 
found  that  the  usual  controls  are  ample  so  far  as  handling 
is  concerned. 

This  gyroscopic  action  will  arise  in  the  case  of  an  aeroplane 
when  for  example  a  tractor  machine  whose  airscrew  and  engine, 
viewed  from  the  C.G.  of  the  machine  is  rotating  in  a  clockwise 
direction,  attempts  a  right-handed  turn.  An  external  couple 
about  a  vertical  axis  is  set  up  owing  to  the  applied  air  forces, 
and  the  axis  of  the  engine  and  the  airscrew  tries  to  set  itself  in 
a  line  with  this  axis,  so  that  there  will  be  a  tendency  for  the 
machine  to  dive. 


258  AEROPLANE    DESIGN 

The  magnitude  of  this  gyroscopic   couple  is  given  by  the 
expression 

Couple  =  -    —ft.  Ibs Formula  79 

where    I  is  the  moment  of  inertia  of  engine  and  airscrew  about  its  axis 
of  revolution  in  absolute  units. 

O  is  the  angular  velocity  of  the  engine  and  airscrew  about  their 
axis  of  revolution  in  radians  per  second. 

w  is  the  angular  velocity  of  the  machine  in  radians  per  second 
at  which  precession  is  forced. 

Experiments  were  carried  out  at  the  Royal  Aircraft  Estab- 
lishment in  order  to  determine  the  magnitude  of  the  gyroscopic 
couple  upon  an  aeroplane  fitted  with  a  100  h.p.  Gnome  Engine. 
The  moment  of  inertia  of  the  engine  was  found  by  weighing 
the  parts  and  measuring  their  distance  from  the  centre,  the 
result  being  checked  experimentally  by  measuring  the  period  of 
oscillation  of  the  engine  when  suspended  by  three  wires. 
Similarly  the  moment  of  inertia  of  the  airscrew  was  determined 
by  suspending  it  bifilarly  and  measuring  its  period  of  oscillation. 
The  results  obtained  for  a  100  h.p.  Gnome  Engine  were:— 
Weight,  270  Ibs.;  M.I.,  114  Ibs.  feet2;  Speed,  1200  r.p.m.  And 
for  an  airscrew:  Weight,  30  Ibs.  ;  M.I.,  150  Ibs.  feet2  ;  whence 
total  moment  of  inertia  for  engine  and  airscrew  is  264  Ibs.  feet2. 

The  gyroscopic  couples  due  to  the  precessional  movements 
involved  both  in  turning  and  pitching  were  determined  as  under. 

(a)  Gyroscopic  Moment  due  to  Turning. — In  the  first  of  these 
cases  the  aeroplane  was  turned  completely  round  in  20  seconds, 
involving  severe  banking  and  a  very  sharp  turn. 

Angular  velocity  of  machine 

2   7T  ,. 

=  w  =  —  =  "314  radian  per  sec. 
Angular  velocity  of  engine  and  airscrew 

=  il  =  2  TT  x  ~  - —  =  125*8  radians  per  sec. 
oo 

whence 

Moment  due  to  gyroscopic  couple 

264  x  125*8  x  "I\A.  f    „ 

=  -  — £LJ?  =  324  ft.  Ibs. 

32-2 

(b)  Gyroscopic  Moment  due  to  Pitching. — The  problem  in  this 
case  necessitates   the  determination   of  the   maximum   angular 


DESIGN    OF   THE    FUSELAGE  259 

velocity  about  the  axis  of  pitch  when  the  elevator  is  suddenly 
deflected  to  its  full  extent.  The  limit  of  this  will  be  determined 
by  that  velocity  at  which  the  pilot  is  just  about  to  be  lifted  from 
his  seat. 

Let     M'  be  the  mass  of  the  pilot. 

6   angle  of  the  path. 

V   the  velocity  of  the  machine  along  the  path. 

r    the  radius  of  curvature  of  the  path. 

M' V2 
Then      M' g  cos  d  =  - 

whence  angular  velocity 

_  V  _  g  cos  0 
~  r  ~       y 

This  is  a  maximum  when  6  is  zero. 

For  the  machine  considered  in  case  (a)  V  is  100  f.p.s. 

o>  =  32-2/100  =  -322  radian  per  sec. 
and  the  moment  due  to  gyroscopic  couple 

_  264  x  125-8  x  '322 

32'2 

=  330  foot  Ibs. 
which  is  of  approximately  the  same  magnitude  as  that  due  to  turning. 

These  figures  indicate  that  there  is  a  twist  set  up  in  the 
engine  structure  which  will  be  communicated  to  the  wings  and 
must  be  opposed  by  a  movement  of  the  control  surfaces.  As 
previously  pointed  out,  this  must  be  borne  in  mind  when 
designing  the  fuselage. 


CHAPTER  VIII. 

DESIGN  OF  THE  CHASSIS. 

Function  of  the  Chassis. — The  most  important  duty  of 
the  chassis  is  to  provide  for  the  attainment  along  the  ground 
of  a  sufficient  speed  to  lift  the  aeroplane  into  the  air.  This  is 
very  easy  to  design  for,  but  the  other  duties  of  a  chassis  are  in 
some  respects  equally  important,  and  must  not  be  lost  sight  of. 
They  are : 

1.  To  make  easy  a  good  landing. 

2.  To    protect  the  airscrew  at    all  times  from  contact  with 

the  ground. 

3.  To    provide   and    permit    of   easy    'taxying'    along   the 

ground. 

4.  To  form  a  firm  base  upon  which  the  machine  may  safely 

stand  at  rest  in  a  wind. 

5.  To  save  the  machine  from  damage,  as  far  as  possible,  in 

the  case  of  a  bad  landing. 

Forces  on  Chassis  when  landing. — The  design  of  the 
Chassis  is  one  of  the  most  difficult  problems  confronting  the 
aeronautical  designer,  for,  while  it  is  desirable  to  obtain  sufficient 
strength  in  the  landing  gear  for  the  machine  to  be  able  to  land 
itself  when  gliding  down  at  its  normal  gliding  angle,  it  must  at 
the  same  time  be  comparatively  light  and  must  offer  as  little 
resistance  to  the  air  as  possible. 

It  will  be  useful  first  to  enumerate  the  forces  acting  upon  a 
machine  when  landing.  Referring  to  Fig.  193  (a)  they  are  : 

1.  The  weight  of  the  machine — W — acting  vertically  down- 

wards through  the  C.G. 

2.  The  lift — w — remaining  on   the  wings   by  virtue  of  the 

forward  velocity. 

3.  The  head  resistance — R. 

4.  The  resistance  of  the  ground  acting  at  the  point  of  contact 

of  the  wheels  and  equal  to  ^  P  where  fj.  is  the  coefficient 
of  ground  friction,  and  may  be  taken  as  0*16,  and  P  is 
the  reaction  at  wheel. 

5.  The  force  due  to  the   momentum — M — depending  upon 

the  velocity  and  the  weight,  and  acting  through  the 
C.G.  of  the  machine. 


DESIGN    OF   THE    CHASSIS  261 

The  fifth  force  causes  a  couple  M  .  d  (d  being  the  perpen- 
dicular distance  from  the  line  of  action  of  M  to  the  point  of 
contact  with  the  ground),  about  the  point  of  contact  tending  to 
overturn  the  machine.  It  is  clear,  therefore,  that  the  position 
of  the  wheels  is  an  important  factor  in  this  connection.  The 
higher  the  C.G.  of  the  machine,  the  farther  forward  must  the 
wneels  be  placed. 

Method  of  locating  Fore  and  Aft  Position  of  Chassis. 
— It  will  be  sufficiently  accurate  for  our  present  purpose  to 
assume  that  both  the  lift  of  the  wings  and  the  resistance  of  the 
machine  act  through  the  C.G.  Then  with  the  notation  shown 
in  Fig.  193  (a),  in  order  to  prevent  nose-diving  of  the  machine 
on  landing,  it  is  necessary  that  the  moment  P  x  must  be  at  least 
equal  to  the  moment  JUL  P  y. 

Consequently  we  have  the  condition 

P.x  >  p-Py 
that  is  -  >  u  Formula  80 

y 

or  tan  0  >  p 

Taking  the  value  of  p  given  above  and  substituting 

tan  6  =  o'i6 
whence         6  =  9° 

In  order  to  allow  for  landing  on  soft  ground  or  upon  a  slope 
this  angle  is  generally  made  equal  to  about  14°,  with  the  axis  of 
the  body  in  the  horizontal  position. 

A  second  method  of  determining  the  fore  and  aft  position  of 
the  wheels  of  the  chassis  is  to  utilise  the  gliding  angle  of  the 
machine  in  the  following  manner : 

Let  C  (Fig.  193  b)  represent  the  position  of  the  C.G.  of  the 
machine  under  consideration.  From  C  drop  a  perpendicular 
C  A  upon  the  ground  line  X  X.  The  distance  of  the  ground  from 
the  horizontal  line  through  the  C.G.  is  governed  by  the  amount 
of  clearance  given  to  the  airscrew,  twelve  inches  being  a  usual 
allowance  for  the  purposes  of  preliminary  design.  Then  set 
out  the  angle  A  C  B  equal  to  the  gliding  angle  of  the  machine. 
As  in  the  first  method,  an  extra  allowance  must  be  made  for 
unforeseen  contingencies,  5°  being  a  common  figure  in  this 
respect.  Therefore  set  out  the  angle  BCD  equal  to  5°,  the  point 
of  intersection  D  with  the  ground  line  X  X  giving  the  required 
position. 


262 


AEROPLANE   DESIGN 


A  third,  but  still  more  empirical  method,  is  illustrated  in 
Fig.  193  (c).  In  this  method  an  angle  of  75°  is  set  off  from  the 
chord  of  the  lower  main  plane  in  order  to  arrive  at  the  required 
position. 


(a* 


^>.p 


FIG.  193. — Methods  of  locating  the  Fore  and  Aft  Position 
of  the  Chassis. 

General  Principles  of  Chassis  Design. — The  first  point 
to  decide  is  the  necessary  factor  of  safety.  A  chassis  cannot 
be  made  strong  enough — for  aerodynamic  reasons — to  stand  up 
to  everything  that  may  possibly  occur.  Provided  that  the  pilot 


DESIGN    OF   THE    CHASSIS  263 

lands  squarely  on  the  two  wheels,  shock  occurs  in  one  of  two 
ways  :  — 

1.  He  does  not  flatten  out  quick  enough  ;  or 

2.  He  flattens  out  too  early,  and  so  *  pancakes  '  down  from  a 

height. 

Considering  the  first  case  and  assuming  that  the  machine 
comes  into  contact  with  the  ground  as  in  a  natural  glide  without 
having  flattened  out  at  all, 

Let  v  be  the  vertical  component  of  V,  the  forward   velocity  of  the 

machine, 

/  be  the  vertical  retardation  on  meeting  the  ground, 
d  be  the  give  of  the  landing  gear  in  feet, 
a  the  angle  of  descent  to  the  horizontal, 
P  be  the  mean  reaction  at  the  wheels  during  landing, 
w  be  the  lift  remaining  on  the  wings,  equal  say  to  two-thirds  of  W, 

the  weight  of  the  machine, 

we  have  p  =  w  +  ^/  -  — 

S  3 


Now  the  vertical  retardation  is  given  by  v2 

vi 
that  is  /=  —  -  =•• 


2  d  2  d 


whence  P  =  W  (  -33  +  Vlsin2«\ 

V  2£df       /      .. 


Formula  81 


By  the  use  of  this  formula  the  reaction  at  the  wheels  during 
landing  can  be  ascertained.  Suppose  a  machine  of  weight  W 
to  be  descending  at  a  slope  of  i  in  6  at  a  speed  of  50  m.p.h. 
To  find  the  reaction  at  the  wheels  for  a  give  of  10"  in  the 
landing  gear  : 

Substituting  in  Formula  81  we  have 


64-4    x     -834 

-  3-03  w 

Assuming  the  shock  absorber  to  be  of  rubber  and  the  force 
to  decrease  uniformly  from  a  maximum  to  zero,  the  maximum 
force  on  landing  will  be  twice  the  average  force.  Hence 
maximum  force  on  landing 

=  6-06  W 


264  AEROPLANE    DESIGN 

that  is,  the  landing  gear  must  be  sufficiently  strong  to  with- 
stand a  ground  reaction  of  about  six  times  the  weight  of  the 
machine. 

From  Formula  81  it  is  obvious  that  the  mean  reaction  will 
decrease  according  as  the  give  of  the  landing  gear  increases,  and 
hence  it  is  necessary  to  provide  a  material  capable  of  absorbing 
the  maximum  amount  of  energy.  This  may  take  the  form  of 
rubber  cord,  steel  springs,  or  pneumatic  cylinders.  Rubber  cord 
is  to  be  preferred  for  small  machines,  because  it  is  light,  cheap, 
easily  workable,  and  easily  replaced  ;  and  it  has  the  further 
great  advantage  of  not  causing  an  elastic  rebound  as  in  the  case 
of  steel  springs,  owing  to  the  energy  of  the  shock  being  suffi- 
ciently absorbed  by  the  viscosity  of  the  rubber. 

Formula  81  also  shows  the  advisability  of  adopting  as  low  a 
value  as  possible  for  the  landing  speed  of  any  machine  under 
design. 

It  will  also  be  observed  from  the  above  example  that  while 
it  is  a  comparatively  simple  matter  to  design  a  chassis  for  a 
machine  possessing  a  low  landing  speed,  it  becomes  increasingly 
difficult  to  do  so  as  the  landing  speed  increases. 

An  efficient  chassis  becomes  heavy  as  the  loading  of  the 
wings  is  increased,  ample  wing  area  leading  to  a  saving  in 
weight  and  resistance.  A  compromise  must  evidently  be  made 
in  most  designs,  and  the  latitude  to  be  allowed  the  pilot  must 
be  assessed  according  to  the  particular  experience  and  practice 
of  the  designer.  An  important  consideration  to  bear  in  mind  is 
-the  necessity  to  preserve  the  machine,  even  if  the  chassis  is 
smashed.  In  this  connection  the  skid  type  of  chassis  would  be 
very  advantageous  were  it  not  for  its  great  resistance  at  high 
speed. 

Types  of  Chassis. — The  various  designs  may  be  roughly 
divided  into  two  groups : 

(a)  Those  with  a  longitudinal  skid  placed  in  front  of,  and 

forming  part  of,  the  chassis  ;  and 

(b)  Those  without  such  skids. 

Of  these  two  groups  by  far  the  greater  number  of  modern 
machines  belong  to  the  second  group,  while  most  of  the  earlier 
types  ^f  machines  possessed  chassis  belonging  to  the  first  group. 

In  the  earlier  types  the  skid  stretched  from  behind  the  C.G. 
of  the  machine  to  either  just  behind  of,  and  in  some  cases  even 
in  front  of,  the  airscrew,  thus  forming  a  backbone  to  the  chassis. 
This  skid  was  fixed  just  a  few  inches  above  the  ground,  and 
provided  a  rigid  stop  to  the  elasticity  of  the  chassis,  thereby 


DESIGN    OF   THE    CHASSIS  265 

preventing  the  airscrew  from  touching  the  ground.     This  type  is 
illustrated  in  Fig.  194. 

The  objection  to  its  use  is  the  heaviness  and  large  air  re- 
sistance of  the  type  of  chassis  involved,  and  the  danger,  either 
in  a  bad  landing  due  to  the  pilot  not  flattening  out  soon  enough, 
or  the  presence  of  rather  rough  ground,  of  the  nose  of  the  skid 
striking  the  ground  directly,  or  even  impaling  itself.  In  the 
event  of  this  happening,  it  is  easy  for  the  aeroplane  to  turn 
completely  over,  owing  to  the  high  position  of  the  C.G.  above 
the  ground.  The  best  way  of  guarding  against  this  contingency 
is  to  protect  the  forward  part  of  the  skid  or  skids  with  small 
extra  wheels.  These  wheels  may  be  very  much  smaller  than 
the  landing  wheels  proper,  but  a  considerable  addition  to  the 
weight,  and,  more  important  still,  a  great  increase  in  the  head 


FIG.  194. — Central  Skid  Chassis. 

resistance,  cannot  be  avoided,  and  therefore  these  wheels  are 
seldom  used. 

The  longitudinal  skid  may  be  either  a  single  central  skid 
fixed  between  the  two  landing  wheels,  or  may  be  made  up  of 
two  lighter  skids  placed  one  in  front  of  each  wheel. 

The  single  or  central  skid  type  of  chassis  has  the  long  central 
skid  fastened  to  the  longerons  of  the  fuselage  by  two  pairs  of 
struts  which  form  a  V»  one  Just  behind  the  airscrew,  and  the 
other  just  in  front  of  the  C.G.  (See  Fig.  194.)  The  forward 
struts  should  be  given  a  rake,  so  that  their  lower  ends  are  in 
front  of  their  upper  ends,  and  the  panels  formed  by  skid,  fuse- 
lage, and  struts  should  be  cross-braced  by  cables.  This  will 
provide  for  the  longitudinal  backwards  component  of  the  force 
of  a  bad  landing.  The  axle  can  also  be  made  divided,  each  half 
being  hinged  at  the  skid,  and  having  a  cable  or  swivelling- rod 
connection  from  just  inside  the  wheel  to  about  half-way  along 
the  skid.  With  this  arrangement,  a  telescopic  shock  absorber 


266  AEROPLANE    DESIGN 

is  needed  from  the  axle  to  the  longerons.  The  skid  should  be 
well  curved  up  in  front  so  as  to  minimise  the  chances  of  impaling. 
This  type  of  chassis  is  suitable  for  heavy  work,  and  can  be 
made  strong  enough  to  withstand  rough  handling  and  very 
bad  landings.  The  V  struts  and  shock  absorbers  at  the  axle 
together  form  a  triple  V  or  M  shaped  girder,  which  can  be 
designed  to  withstand  a  large  sideways  force,  such  as  occurs  in 
a  bad  landing  on  one  wheel.  High  resistance  is  unavoidable 
owing  to  the  multiplicity  of  its  parts,  so  that  it  is  unsuitable 
for  high-speed  work  unless  great  strength  is  required.  If  the 
skid  is  continued  under  the  airscrew,  protection  is  afforded  to 
that  member.  There  is  one  point  of  weakness  which  requires 
attention  :  that  is,  the  inability  of  the  forward  chassis  struts  to 
withstand  any  considerable  transverse  force.  As  wide  an  angle 


FIG.  195. —  Double  Skid  Chassis. 

V  as  possible  should  be  sought  for  here,  and  consequently,  if 
the  longerons  converge  considerably  towards  the  front  of  the 
fuselage,  the  forward  struts  may  require  to  be  attached  to  them 
some  distance  back  from  the  engine  plate  or  fuselage  nose,  at  a 
position  where  the  fuselage  is  still  wide.  Although  the  forward 
rake  of  these  struts  helps  in  this  respect,  their  bottom  ends  may 
nevertheless  be  a  long  way  behind  the  airscrew  in  the  case  of 
an  overhung  rotary-engined  machine.  Consequently  it  is  not 
always  possible  to  prolong  the  skid  under  the  airscrew,  owing 
to  the  large  bending  moment  which  may  occur  in  the  skid  due 
to  this  leverage.  Apart  from  this,  it  will  be  found  advisable  to 
use  a  strong  skid  in  this  central  type. 

The  double  skid-  type  of  chassis  (Fig.  195)  is  comprised  of 
two  lighter  longitudinal  skids,  connected  to  each  other  and  the 
fuselage  with  struts,  the  whole  structure  being  braced  together 
in  the  usual  manner. 

Telescopic  shock  absorbers  are  out  of  place  in  this  design, 


DESIGN   OF   THE   CHASSIS 


267 


elasticity  being  provided  by  wrapping  rubber  cord  round  the 
outer  ends  of  the  axle,  just  inside  the  wheel  and  the  fixed  trans- 
verse strut.  This  type  is  lighter,  and  has  less  resistance  than 
the  central  skid  type,  owing  to  the  decreased  number  of  parts, 
and  to  the  abolition  of  the  telescopic  shock  absorber ;  but  it  is 
not  so  flexible,  and  is  weaker  in  many  ways,  and  therefore  not 
suitable  for  heavy  rough  work.  On  the  other  hand  it  is  stronger 
than  the  central  design  as  regards  side  force  well  forward,  as  its 
braced  square  panel  forward  is  much  superior  to  the  simple  V  5 
but  it  may  be  argued  on  the  contrary  that  it  is  more  liable  to 
such  a  force.  It  is  not  much  use  to  prolong  the  double  skids 


(a) 


196 


Landing  Chassis  Details. 


forward  past  the  airscrew.  The  prolonged  central  skid  is  a 
protection  chiefly  against  a  localised  hillock  on  the  ground  ;  the 
double  skids,  if  prolonged,  would  only  be  useful  against  a  bank, 
as  a  small  hillock  might  easily  pass  between  them  and  cause 
an  accident. 

The  chassis  just  considered  is  a  half-way  house  between  the 
heavy,  single  skid  type,  and  the  light,  skidless  design  which  con- 
stitutes the  second  group.  (See  Figs.  197  and  198.)  In  this 
group  there  is  no  limit  stop  or  positive  protection  for  the  airscrew. 
The  axle  is  connected  to  the  lower  longerons  by  a  pair  of  struts 
on  each  side,  forming  two  V's  longitudinally  placed.  The  two 
struts  forming  each  V  are  united  at  their  lower  ends  by  a  steel 


268 


AEROPLANE    DESIGN 


fitting,  which  also  provides  a  vertical  slot  for  up-and-down 
movement  of  the  axle.  See  Fig.  196  (d).  If  this  slot  be  made 
with  a  beaded  edge,  and  the  axle  fitted  with  four  collars,  the 
axle  can  be  arranged  to  act  the  part  of  a  transverse  strut.  The 
resistance  and  weight  are,  in  this  case,  reduced  to  a  minimum 
for  a  fixed  chassis  ;  there  are,  indeed,  only  five  members,  and 
two  of  these  are  in  protected  positions.  Skill,  however,  is 
required  in  manoeuvring  over  the  ground  so  as  to  keep  the 
airscrew  safe,  and,  with  this  end  in  view,  the  wheels  may  with 
advantage  be  set  somewhat  further  forward  than  with  the  other 
types,  in  order  to  give  a  larger  tail  moment. 

When   landing  on  one  wheel  there  is  generally  a  resulting 
side  blow  on  the  chassis,  and  in  order  to  resist  this  it  is  cus- 


Fig.  197. — Landing  Chassis  of  Bristol  Fighter. 


tomary  to  introduce  cross  bracing  between  the  axle  and  the 
fuselage. 

This  type  is  eminently  suitable  for  light,  high-speed  work, 
and  owing  to  its  great  advantages  as  regards  light  weight  and 
low  resistance,  its  use  should  always  be  carefully  considered 
before  another  type  is  adopted.  Some  excellent  examples  of 
this  type  of  chassis  are  shown  in  Figs.  196,  197,  198. 

Fig.  196  shows  the  details  of  the  chassis  of  the  Airco  4 
machine.  Each  pair  of  side  struts  is  made  of  solid  wood,  and  at 
their  lower  ends  vertical  strut  shoes,  which  carry  the  wheel,  axle, 
and  fittings  for  the  rubber  shock  absorbers,  are  fixed.  The  axle 
itself — Fig.  196  (c  and  e) — rests  between  two  cross  struts  of 
wood,  which  are  shaped  to  a  streamline  form  as  shown.  The 
total  weight  of  this  chassis  is  119  Ibs. 


DESIGN   OF   THE   CHASSIS 


269 


The  landing  chassis  for  the  Bristol  Fighter  is  shown  in 
Fig.  197,  and  Fig.  198  shows  this  type  as  used  in  a  standard 
American  training  machine.  The  method  of  construction  is 


Reproduced  by  courtesy  of  '  Flight. ' 

FIG.  198. — Wright-Martin  Landing  Chassis. 


clearly  shown  in  these  figures.  An  illustration  of  a  chassis 
suitable  for  heavy  machines  is  shown  in  Fig.  199,  which  depicts 
the  complete  chassis  of  the  Handley-Page  machine  O-4OO. 


FIG.  199. — Chassis  of  Handley-Page  Machine. 

Stresses  in  Chassis  Members. — The  determination  of  the 
stresses  in  the  V  type  of  chassis  offers  little  difficulty.  The 
stresses  in  the  struts  are  obtained  by  resolving  the  reaction 


270 


AEROPLANE    DESIGN 


J  P  at  the  wheel  along  the  required  direction,  or  by  drawing 
a  stress  diagram  as  shown  in  Fig.  200,  care  being  taken  to  use 
the  component  of  the  reaction  in  the  plane  of  the  struts,  as 
determined  by  means  of  Formula  Si. 

The  maximum  side  shock  likely  to  occur  on  the  machine 
may  be  taken  as  one-fifth  of  the  maximum  vertical  reaction  at 
each  wheel.  The  cross  bracing  should  be  designed  to  withstand 
this  load. 


FIG.  200. — Stress  Diagram  and  Bending  Moment  Diagram  for 
Landing  Chassis  with  Divided  Axle. 


The  stress  on  the  axle  may  be  simply  determined  in  the 
following  manner  : — 

i.  Continuous  Axle  (Fig.  201). — Let  the  distance  between 
the  centre  H  of  the  hub  and  the  centre  S  of  the  shock  absorber 
elastic  be  a,  and  that  between  the  latter  point  and  the  central 
longitudinal  plane  of  the  machine  be  b.  The  bending  moment 
on  the  axle  is  due  to  the  couple  \  P  a,  and  increases  from  zero 
at  the  hub  centre  to  J  P  a  at  the  point  s.  From  S  it  is  constant 
until  the  other  shock  absorber  centre  is  reached,  whence  it 
decreases  to  zero  at  the  centre  of  the  other  hub.  The  axle  in 
this  case  may  well  be  made  of  uniform  strength,  except  for  the 
portions  H  to  S,  which  may  be  strengthened  against  shear.  In 


DESIGN    OF   THE    CHASSIS 


27  F 


the  event  of  landing  on  one  wheel,  if  Q  be  the  load  on  the  wheel,, 
the  bending  moment  increases  from  zero  at  H  to 

Q  x  a  x  2  b 
2  b  +  a 

at  S,  and  from  there  decreases  again  to  zero  at  the  point  of 
attachment  of  the  other  shock  absorber.  There  is  then  a  tension 
in  the  other  shock  absorber  equal  to  Q  a  I  (2  b  +  a)y  which  must 
be  provided  for. 


B.M      DiACRAH 

FIG.  201. — B.M.  Diagram  for  Landing  Chassis  with  Continuous  Axle. 


2.  Divided  Axle  (Fig.  200). — In  this  case  the  bending  moment 
gradually  diminishes  from  ^  P  a  at  S  to  zero  at  M.  The  axle 
may  therefore  be  made  lighter  towards  the  centre  so  long  as  it 
is  able  to  take  the  constant  shearing  force  between  the  central 
plane  and  S,  equal  in  magnitude  to  Qa/  (a  +  b).  Alternatively 
the  portion  on  each  side  of  S  subjected  to  large  bending  moment 
may  be  reinforced.  It  is  important  to  keep  S  as  near  to  H  as 
possible.  With  a  divided  axle  it  is  necessary  to  haye  a  wire 
leading  from  the  junction  of  the  cross  bracing  wires  to  the 
central  hinge  fittings,  in  order  to  counteract  the  downward 
force  at  the  hinge  due  to  the  load  on  the  wheels. 

Shock  Absorbers. — The  two  main  types  of  shock-absorbing: 
devices  are — 

(a)  Rubber  shock  absorbers. 
b    Oleo  shock  absorbers. 


2*72  AEROPLANE    DESIGN 

The  first  type  is  used  much  more  extensively  than  the  second, 
principally  on  account  of  its  lightness,  ease  of  construction,  and 
its  cheapness.  It  has  this  disadvantage,  however,  that  the 
mechanical  properties  of  rubber  vary  very  considerably,  and  are 
likely  to  deteriorate  with  time.  Some  interesting  experiments 
upon  a  rubber  shock-absorbing  device  were  carried  out  by 
Hunsaker  at  the  Massachusetts  Institute  of  Technology. 

A  shock  absorber  of  the  type  shown  in  Fig.  202  was  fitted 
with  twelve  rubber  rings  2"  x  2"  x  5/16"  each  passing  over  a  J" 
steel  pin.  Table  XLII.  shows  the  elongation  corresponding  to 
a  series  of  loads. 


FIG.  202. 


TABLE 

XLII.  —  ELONGATION 

OF  SHOCK  A] 

Load. 

First  loading. 

Second  loading. 

1000  Ibs. 

•22" 

•48" 

2000       „ 

•78" 

I'25" 

3000       „ 

1*40" 

1-98" 

4000       „ 

2'o8" 

2'45" 

3000       „ 

r98" 

2-26" 

2000       „ 

1-57" 

174" 

1000       „ 

•68" 

•70" 

Third  loading. 

•52" 

i'37" 
2*12" 

2  "60" 

2-45" 


Finally  the  absorber  was  tested  to  destruction  and  failed  at 
9750  Ibs.,  with  a  corresponding  extension  of  5*06".  The  pins 
failed  by  shearing  with  the  rubber  rings  still  unbroken.  The 
effect  of  hysteresis  is  brought  out  clearly  in  the  above  figures, 
the  rubber  not  contracting  as  rapidly  as  it  extends.  The  area  of 
the  hysteresis  loop  represents  the  work  done  on  the  rubber 
which  is  not  restored  and  is  a  measure  of  the  shock-absorbing 
quality  of  the  rubber.  Moreover,  it  will  be  seen  that  the 
hysteresis  loss  diminished  with  each  loading.  The  stress  in  the 
rubber  rings  when  the  bridge  failed  was  650  Ibs.  per  square  inch. 
In  a  subsequent  test  they  failed  at  a  stress  of  900  Ibs.  per 
square  inch. 

Reference  to  Formula  81  shows  that  an  increase  of  'give'  of 
the  shock-absorbing  device  reduces  the  reaction  at  the  wheels, 


DESIGN    OF   THE   CHASSIS  273 

hence  greater  elasticity  of  the  rubber  is  needed  to  reduce  landing 
shock  on  the  chassis.  Such  increase  of  elasticity  would  have  the 
further  advantage  of  relieving  the  jolting  of  the  machine  when 
running  along  the  ground. 

DESIGN  OF  A  RUBBER  SHOCK  ABSORBER. — In  order  to 
determine  the  number  of  rubber  rings  required  to  absorb  the 
landing  shock  of  a  machine  it  is  necessary  to  equate  the  work 
done  in  stretching  the  rubber  to  the  energy  of  the  machine  at 
the  instant  of  landing.  For  example,  to  take  the  case  of  the 
machine  referred  to  on  page  263. 

Kinetic  Energy  of  the  machine  on  landing 

=  (W  -  w)  (V  sin  a)2  =  -33  W  x  i22 

2g  64 

=  74  W 
Potential  Energy  of  the  machine  on  landing 

=  (W  -  w)  x  '  give '  of  gear  =  -33  W  x  '834 

=    -275W 
whence  Total  Energy          =  1-015  W 

To  determine  the  stretch  of  the  shock-absorbing  device  we 
apply  Formula  3,  so  that 

PL 


Extension 


AE 


and  if  n  be  the  number  of  rings  of  rubber  cord  of  f  "  diameter, 
and  the  diameter  of  each  ring  assumed  to  be  6",  we  have 


=  'I4% 

For  good  quality  shock  absorber  elastic  E  is  taken  as  300  Ibs. 
per  square  inch. 

In  the  above  expression 

P  =  average  load  on  the  shock  absorber 
=  half  total  reaction  at  wheels 


=  51-51  W 

,  -142  x  1-51  W 

whence         x  —  —  ^  -  -  - 


n 


3  FIG.  203  (a) 


Reproduced  by  courtesy  of  l  Flight: 

FIG.  203  (b}. 


FIG.  203  (c) 


Types  of  Shock  Absorbers. 


FIG.  203  (ff). — Shock  Absorber  Device,  and  Streamlining  of  Axle 
of  Landing  Chassis. 


Reproduced  by  courtesy  of  '  Flight.'1 

FIG.  203  (e) 


276  AEROPLANE    DESIGN 

Further  equating  the  total  energy  to  the  work  done 
1-015  W  =  P-  — 


12 

Substituting  for  x  and  P 

1-51  W(-i42  x  1-51  W) 

12  n 
whence          n  =  '0267  W  Formula  82 


3  — B 


-A 


1-015 


FIG.  204. 


Therefore,  for  a  machine  weighing  2000  Ibs.,  54 
rings  of  rubber  of  the  size  mentioned  would  be 
required.  In  this  calculation  no  allowance  has 
been  made  for  the  energy  absorbed  by  the  resilience 
of  the  pneumatic  tyres. 

In  practice,  the  most  general  method  of  ap- 
plying the  rubber  is  to  coil  a  long  length  around 
the  axle  and  the  main  chassis  struts  respectively. 
The  number  of  turns  required  will  correspond  to 
the  number  of  rings  as  calculated  from  the  above 
formula,  plus  any  turns  necessary  for  starting  and 
ending. 

Illustrations  of  rubber  shock-absorber  devices 
are  shown  in  Fig.  203. 

OLEO  SHOCK  ABSORBERS. — These  in  general 
consist  of  two  telescopic  steel  tubes,  the  outer  one 
serving  as  a  cylinder  in  which  oil  is  maintained 
at  a  fixed  level,  whilst  the  inner  tube  is  attached 
to  the  body  and  acts  as  a  piston.  The  inner  tube 
or  piston — see  Fig.  204  (B) — carries  a  spring- 
loaded  valve  which  covers  ports  round  the  lower 
part  of  the  tube.  The  cylinder  below  the  valve  is 
filled  with  oil.  When  landing  occurs  and  the  tubes 
are  compressed,  the  oil  passes  through  a  series  of 
small  holes  into  the  upper  cylinder.  If  the  shock 
of  landing  exceeds  a  certain  figure,  the  spring- 
loaded  valve  opens  and  provides  an  additional 
passage. 

Particulars  of  an  Oleo  Leg,  designed  by  the 
R.A.F.,  are  given  in  the  Report  of  the  Advisory 
Committee  for  Aeronautics,  1912-13,  as  follows  : 
During  flight  the  lower  tube  or  cylinder  con- 
taining the  oil  drops  through  1 1  inches.  When  the 
machine  (a  B.E.  2)  strikes  the  ground  the  oil  first 
passes  into  a  small  central  air  chamber  and  after- 
wards through  three  4  millimetre  exit  holes.  If 


DESIGN   OF   THE   CHASSIS  277 

the  velocity  of  impact  with  the  ground  is  sufficiently  great 
so  that  the  resistance  of  the  oil  passing  through  these  holes 
is  enough  to  raise  the  oil  pressure  to  640  Ibs.  per  square 
inch,  the  spring-loaded  valve  opens  and  allows  the  oil  an 
additional  passage. 

The  arrangement  was  designed  so  that  after  the  first  two 
inches  of  travel  the  resistance  remains  constant,  and  equal  to 
two  and  a  half  times  the  weight  of  the  machine.  The  vertical 
travel,  excluding  the  first  2",  was  13",  so  that  if  the  pressure 
remained  constant  the  total  energy  absorbed  was  4300  ft.  Ibs., 
and  consequently  the  machine  could  land  without  damage  with 
a  vertical  velocity  of  13  feet  per  second.  In  addition  to  the 
oil  and  air  gear,  strong  spiral  springs  carry  the  weight  of  the 
machine  when  running  along  the  ground. 

The  Tail  Skid. — The  tail  skid,  which  is  situated  at  the  rear 
end  of  the  fuselage,  provides  the  necessary  point  of  support  for 
the  rear  portion  of  an  aeroplane  when  the  machine  is  resting  on 


FIG.  205. 

the  ground.  There  are  several  different  types  of  skids  in  actual 
use,  examples  of  which  are  shown  in  Figs.  205-208. 

The  simplest  form  is  that  shown  in  Fig.  205.  In  this  type 
the  movement  of  the  tail  skid  relative  to  the  body  of  the  machine 
is  confined  to  the  vertical  plane.  The  skid  itself  is  usually  made 
of  ash,  and  is  provided  with  a  steel  shoe.  The  shock  absorber 
device  is  composed  of  rubber  cord.  Another  example  of  this 
type  is  shown  in  Fig.  206. 

Another  type  of  tail  skid  is  that  in  which  the  tail  skid  is  free 
to  rotate  about  a  vertical  axis.  The  skid  can  then  set  itself  at  any 
angle  laterally,  and  can  therefore  follow  the  curve  traced  out  by 
the  aeroplane  in  its  motion  over  the  ground.  Such  movement 
makes  it  much  more  convenient  to  manoeuvre  the  machine  when 
'  taxying '  before  flying  or  after  alighting.  Examples  of  this 
type  of  skid  are  shown  in  Figs.  207,  208. 


FIG.  206. — Example  of  Tail  Skid  for  Large  Machine. 


FIG.  207. 


FIG.  208 


DESIGN    OF   THE    CHASSIS  279 

In  Fig.  207  the  shock  absorber  device  is  of  rubber,  which  is 
placed  in  tension  when  the  machine  is  upon  the  ground.  A 
variation  of  this*  type  is  shown  in  Fig.  208.  In  this  skid  the 
shock-absorbing  device  is  composed  of  steel  springs  which  are 
subject  to  compression  when  in  use.  Such  an  arrangement  is 
more  efficient  mechanically  than  the  previous  types  shown,  for 
it  leads  to  a  much  smaller  reaction  at  the  fulcrum. 

Streamlining  the  Chassis. — In  general,  the  question  of 
streamlining  the  chassis  must  be  carefully  considered,  and  all 
parts  should  be  given  a  streamline  form  wherever  possible.  The 
resistance  of  the  under-carriage  is  generally  an  important  item, 
particularly  in  the  case  of  high-speed  scouts.  Attempts  have 
also  been  made  to  design  a  chassis  which  can  be  drawn 
within  the  fuselage  during  flight. 


CHAPTER  IX. 
DESIGN  OF  THE  AIRSCREW. 

Methods  of  Design. — The  problem  of  airscrew  design  has 
been  approached  by  analytical  arid  by  empirical  methods  The 
two  principal  methods  of  analytical  attack  are  : 

(i.)  Examination  of  the  air  flow  through  the  airscrew  and 
the  determination  of  expressions  for  its  change  in 
momentum  and  energy. 

(ii.)  Consideration  of  the  actual  forces  set  up  upon  the 
blades. 

The  first  method  may  be  called  the  classical  method,  and 
was  the  method  developed  by  Rankine,  Froude,  and  others 
for  application  in  the  first  instance  to  the  design  of  marine 
propellers. 

The  second  method  is  known  as  the  blade  element  method, 
and  has  been  specially  developed  for  application  to  airscrews, 
the  pioneers  in  this  case  being  Drzewiecki  and  Lanchester. 

In  both  cases  the  premises  are  somewhat  obscure,  and  the 
conclusions  therefore  correspondingly  uncertain.  It  should  be 
noted,  however,  that  the  second  method  is  concentrated  on  the 
airscrew  itself  from  first  to  last,  and  so  leaves  the  designer  with 
something  definite  to  work  upon,  even  if  the  data  are  not  suffi- 
ciently accurate  for  his  purpose.  The  design  of  airscrews,  there- 
fore, is  best  attempted  along  the  more  modern  line  of  thought, 
which  is  generally  known  as  the  Blade  Element  Theory. 
This  method  is  based  upon  laboratory  experiments  upon  aero- 
foils, about  which  a  vast  amount  of  information  is  available 
from  the  force  shape  point  of  view ;  whereas  very  little  definite 
information  concerning  the  flow  of  air  past  an  aerofoil  is  avail- 
able in  a  quantitative  form  that  can  be  applied  to  the  design  of 
an  airscrew. 

The  first  principles  of  the  method  are  familiar  to  most 
engineers  :  an  element  of  the  blade  is  taken  at  any  radius  from 
the  centre  of  rotation,  say  a  section  of  width  dr  at  a  radius  r,  as 
shown  in  Fig.  209  ;  and  this  section  is  then  studied  separately 
while  still  considered  as  joined  to  the  whole.  It  is  assumed  that 
this  element  operates  like  a  small  aerofoil,  the  aerodynamic 
properties  of  which  can  be  easily  determined,  as  explained  in 


DESIGN    OF   THE  AIRSCREW 


281 


Chapter  III.  The  whole  airscrew  is  then  treated  as  a  summa- 
tion of  such  elements,  and  the  forces  on  the  whole  airscrew  as 
a  summation  of  the  forces  such  as  those  upon  the  small  element 
studied,  applying  to  successive  subdivisions  of  the  blade  such 
corrections  for  velocity,  leverage,  &c.,  as  may  be  necessary. 

It  is  first  essential  to  realise  the  path  of  the  blade.  This, 
being  a  motion  of  uniform  rotation  and  of  uniform  translation, 
is  a  helix,  similar  to  a  very  deep-cut  coarse  pitch  screw  thread. 
Fig.  210  is  a  sketch  of  such  a  path.  It  should  be  noticed  that 
as  the  radius  is  increased,  so  the  resultant  or  helical  velocity  is 
increased.  The  forward  velocity  of  the  airscrew,  however,  is 
uniform  for  every  point  on  it,  and  therefore  the  pitch  is  constant, 


Fi<5  909 


'l«00f  CP» 


(- TTD 


unless  expressly  made  otherwise.  The  geometric  pitch  is  the 
length  along  the  axis  which  the  airscrew  would  move  for  one 
revolution,  if  the  fluid  through  which  it  moved  suffered  no 
translation,  as  for  example  if  the  screw  worked  in  a  fixed  nut. 
If  the  fluid  behaved  in  this  manner  we  could  represent  the 
motion  of  our  element  as  taking  place  along  the  hypotenuse  of 
the  triangle  shown  in  Fig.  21 1 ;  having  for  its  sides  the  pitch  (D), 
and  the  length  of  the  particular  circumference  chosen  (2  wr). 
The  motion  of  the  wing  tip  would  of  course  be  given  by  sub- 
stituting TT  D  for  the  latter  side,  where  D  is  the  diameter  of  the 
airscrew.  The  above  conditions  of  working  are  most  nearly 
realised  in  practice  when  the  airscrew  is  so  working  that  there 
is  no  thrust  on  the  shaft.  The  axial  advance  for  one  revolution 


282 


AEROPLANE    DESIGN 


under  these  circumstances  is  termed  the  experimental  mean 
pitch  (/).  Tn  practice,  however,  the  airscrew  is  usually  exerting 
a  pull,  and  the  axial  advance  per  revolution  is  considerably  less 
owing  to  the  velocity  impressed  on  the  air.  If  V  feet  per  second 
be  the  translational  velocity  of  the  airscrew,  revolving  at  N 
revolutions  per  second,  the  actual  effective  pitch  is  V/N  feet. 
The  amount  by  which  this  quantity  is  less  than  P  is  termed  the 
*  slip,'  and  averages  between  20%  and  30%.  It  is  convenient  to 
think  of  this  in  terms  of  the  dimensions  of  the  airscrew,  and  so 
the  term  '  slip  ratio '  is  introduced,  and  we  have 


P  - 


Slip  ratio  = 


N 


The   true   path   of  the  blade  element   is  as  represented    in 


FIG.   212. 


FIG.  213. 


Fig.    212,   where   the   dotted    lines   show    the    variation    from 
Fig.  211. 

Now  the  blade  element  theory  is  built  upon  aerofoil  data, 
and  remembering  this,  we  may  define  the  position  of  the  element 
as  shown  in  Fig.  213.  A  is  the  angle  of  the  helix,  and  is  equal 
to  the  angle  whose  tangent 

V 


0  is  the  angle  of  incidence  of  the  aerofoil  element  to  its  path, 
R  is  the  resultant  air  force  upon  it,  0  is  its  inclination  to  the 
perpendicular  to  its  path,  L  is  the  aerofoil  lift  along  this  per- 
pendicular to  the  path,  D  is  the  drag  or  component  of  R  along 
the  path.  The  thrust  t  is  the  component  of  R,  along  the  direction 
of  the  translational  velocity,  that  is,  along  X  Y.  Hence  we  have 

/  =  R  cos  (A  +  0) 


DESIGN    OF   THE   AIRSCREW  283 

The  resistance  to  rotation,  that  is,  the  torque  q  on  the  shaft,  is 
proportional  to  the  component  of  R  along  the  line  xz  (the 
direction  of  rotative  velocity),  so  that 

q  =  R  sin  (A  4-  </>)  r 
and  the  efficiency  of  the  element 

R  cos  (A  +  0)  V 


~  R  sin  (A  +  0)  27rrN 

=  cot  (A  +  0)  tan  A     .  ...........  Formula  86  (a) 

Aerofoil  data  are  given  in  the  form  of  the  absolute  co- 
efficients of  the  Lift  and  the  Drag.  From  these  we  can  obtain 
the  values  of  the  absolute  coefficients  of  resultant  force,  Kr  and 
of  0,  by  making  use  of  the  following  relationships  :  — 


Kr  =   V  Kx2  +  Ky2 

Kx 

and       0  =  tan~r   TT~ 

Ky 

If  b  is  the  breadth  of  the  blade  where  the  element  is  chosen, 
the  thrust  on  each  element  may  be  written 

d"p=  Kr  •  -   •  b  •  dr  •  v2  •  cos  (A  +  0) 

6 

where     v  =  velocity  along  helical  path 


V 
V 
1 


-  _lJL 

sin  A 


whence  Jflp=  K.^-          cos  (A  + 


sin2  A 

and  total  thrust  = 

cos  (A 


"PT^     A/         ^Kx 

*  Ky  V  i  +  (K) 


Formula  83 
where  n  =  number  of  blades. 


284  AEROPLANE    DESIGN 

Similarly  the  torque  q  on  any  element  is  given  by 

q  =  Kr  •  £  .  £  .  dr  .  z/2  sin  (A  +  0)   .  r 

o 


-  K 


/        /Kx\2      p  V,2 

/y   i  +  IjF"  )     '        '  ^   •  >*  •  ^^^ i  T    '  S" 


and  total  torque  = 


Q  -  „ 


Formula  84 

An  examination  of  these  expressions  for  the  total  thrust  and 
the  total  torque  of  an  airscrew  indicates  that  in  order  to  evaluate 


FIG.  214. — Aerodynamic  Characteristics  for  Airscrew  Sections. 

the  integrals,  it  is  necessary  to  know  the  aerodynamic  charac- 
teristics of  a  number  of  suitable  aerofoil  sections.  The  data 
given  on  pages  67  -  70  relating  to  the  sections  illustrated 
will  be  found  very  useful  in  this  connection.  From  the  data 
there  given  the  curves  shown  in  Fig.  214  have  been  drawn.  It 
is  seen  from  Fig.  53  that  the  most  efficient  angle  of  incidence, 
that  is,  the  angle  giving  the  maximum  ratio  Ky/Kx,  for  these 
sections,  is  in  the  neighbourhood  of  3°.  Consequently  the  angle 
of  attack  (0)  for  the  airscrew  elements,  if  these  sections  be  used, 
should  be  3°.  Using  this  angle  of  incidence,  the  curves  shown 


DESIGN    OF   THE   AIRSCREW 


285 


in  Fig.  214  have  been  drawn,  giving  the  values  of  Ky  and  Ky/Kx 
plotted  against  the  ratio  Thickness/Chord.  The  value  of  this 
proceeding  will  be  evident  shortly.  It  should  be  observed  here 
that  on  account  of  the  loss  in  efficiency  of  an  airscrew  when 
climbing,  it  is  sometimes  advisable  to  adopt  a  smaller  angle  of 
attack  than  the  angle  of  maximum  efficiency,  in  order  to  mini- 
mise this  loss  when  climbing.  Such  an  arrangement  leads  to 
reduced  efficiency  at  top  speed,  which  is  counterbalanced  by  an 
increased  efficiency  when  climbing.  The  advisability  of  such 
procedure  naturally  depends  upon  the  desired  performance,  and 
the  designer  must  compromise  in  order  to  get  the  results  desired 


v 


fi-ar,  Ccrtr*) 


Fig.  215. — Design  Data  for  2-bladed  Airscrews. 


in  any  particular  case.  It  is  on  this  account  that  an  airscrew  in 
which  the  angles  of  the  blade  are  adjustable  in  accordance  with 
the  conditions  of  flight  prevailing  would  offer  considerable 
advantages,  and  would  lead  to  a  much-increased  all-round 
efficiency.  This  problem  of  the  variable  pitch  airscrew  is  re- 
ceiving much  attention,  and  will  undoubtedly  be  solved  in  the 
very  near  future. 

A  second  factor  involved  in  the  evaluation  of  the  integral  is 
the  ratio  £/£max.  This  ratio  represents  the  width  of  the  blade 
at  any  section  in  terms  of  the  maximum  width  of  the  blade,  and 
its  value  is  dependent  upon  the  plan  form  adopted. 

Figs.  215  and  216  represent  an  analysis  of  several  types  of 


286 


AEROPLANE    DESIGN 


airscrews  which  have  proved  successful  in  practice,  the  curves 
showing — 

(a)  The  ratio  bjbm3LK 

(b]  The  ratio  maximum  thickness/chord, 

for  all  points  along  the  blade.  These  curves,  together  with  those 
shown  in  Fig.  214  give  all  the  necessary  data  for  the  design  of 
a  successful  airscrew,  and  their  application  to  such  design  will 
be  fully  explained  in  this  chapter. 

Referring  to  the  expression  for  total  torque  (Formula  84),  it 
is  seen  that  by  inserting  the  values  of  Ky,  Kx,  <V#max  ^or  a 
number  of  sections  along  the  blade,  the  various  values  of  the 


\ 


ffadiua     (Fr-ocHor)    frtm 

FIG.  216. — Design  Data  for  4-bladed  Airscrews. 

expression  at  these  sections  can  be  evaluated,  and  the  torque 
curve  for  the  airscrew  can  then  be  drawn.  The  torque  available 
from  the  aero-engine  at  maximum  efficiency  is  given  by  the 
relationship 

H'Rx  «°       Formula  85 


Torque      = 

where  N    = 
H.P.    = 


27rN 

number  of  revolutions  per  second 
horse-power  of  engine. 

By  equating  this  torque  to  that  given  by  Formula  for  torque 
of  the  airscrew,  the  requisite  value  of  £max,  the  maximum  blade 
width  is  determined.  Having  determined  the  maximum  blade 
width,  the  width  at  all  sections  immediately  follows  from  Figs. 
215,  216. 


DESIGN    OF   THE   AIRSCREW  287 

Further,  when  the  maximum  blade  width  has  been  deter- 
mined, the  thrust  can  be  calculated  by  the  use  of  the  expression 
for  total  thrust  (Formula  83). 

Finally,  the  overall  efficiency  of  the  airscrew  will  be  given  by 
the  expression 

T  V 
e  —  Formula  86 

27TNQ 

where     V  =  translational  velocity  of  the  machine 
T  =  thrust  of  the  airscrew 
Q  =  torque  of  the  airscrew 
N  =  revolutions  of  the  airscrew. 

Unfortunately  the  premises  are  not  so  adequate  as  a  super- 
ficial glance  at  the  above  formulae  would  seem  to  indicate.  The 
chief  causes  of  error  may  be  summarised  as  under,  and  must  be 
taken  into  account  by  the  designer. 

1.  Air  is  set  in  motion  by  the  airscrew  before  the  disc  of  the 

airscrew  is  actually  reached. 

2.  Aerofoil  data  may  not  be  directly  applicable  in  the  case 

of  the  very  high  speeds  obtaining  with  airscrews. 

3.  '  Wing  tip  losses  '  are  very  important,  as  the  tip  is  the 

most  effective  part  of  the  blade  of  the  airscrew. 

4.  Allowances  are  necessary  for  the  root  of  the  blade,  partly 

because  it  must  be  designed  primarily  for  strength,  and 
not  for  efficiency,  and  partly  because  of  the  boss  and 
other  obstructions. 

It  may  be  observed  that  research  work  is  in  progress  upon 
all  these  doubtful  points.  To  allow  for  the  first  it  is  necessary 
to  measure  the  'velocity  of  inflow'  at  various  radii,  and  then 
modify  the  analysis  to  suit.  Information  was  given  on  this  point 
in  a  paper  read  before  the  Aeronautical  Society  by  M.  A.  S. 
Riach  in  19 r/.  In  this  connection  Formula  86  (a)  should  be 
plotted  for  various  values  of  A,  when  it  will  become  apparent 
that  the  efficiency  of  the  element  depends  upon  the  radius. 

The  second  point  will  become  clearer  the  more  model  ex- 
periments are  carried  out  upon  airscrews  having  blades  of  known 
aerofoil  sections. 

The  third  point  suggests  a  rounded  tip  in  preference  to  a 
square  end  ;  and  the  fourth  point  indicates  that  it  will  in  most 
cases  be  hardly  worth  while  to  trouble  about  obstructions  to 
flow  massed  round  the  shaft. 

When  setting  out  the  plan  form  of  the  blade,  care  should  be 
taken  to  eliminate  twisting  as  far  as  possible.  This  is  effected 
by  arranging  the  moments  of  the  forces  on  the  blade  elements 
about  a  line  drawn  along  the  length  of  the  blade,  so  that  these 


288  AEROPLANE   DESIGN 

moments  balance  one  another.  For  this  purpose  the  aerofoil 
data  giving  the  C.P.  position  for  each  blade  element  used  must 
be  employed. 

Experimental  Method  of  Design.  —  When  using  this 
method  of  design,  small  model  airscrews  are  constructed  and 
tested  experimentally,  and  from  the  results  obtained  the  pro- 
bable performance  of  a  full-sized  airscrew  of  similar  design  is 
deduced  from  the  laws  of  geometrical  similitude.  The  following 
formulae  are  assumed  to  hold  good  for  geometrically  similar 
airscrews  :  — 

Thrust  =  C  N2  D4 

Horse-power  =  K  N3  D5 

where         N  =  airscrew  revolutions  per  second 
D  =  airscrew  diameter  in  feet. 

C  and  K  are  constants  depending  upon  the  ratio  of  the 
circumferential  blade  tip  velocity  to  the  translational  velocity  — 
that  is,  they  are  proportional  ND/V. 

Also  since  the  efficiency  of  the  airscrew 

Thrust  x  Forward  Velocity 
Horse-power 


where  M  is  a  constant. 

It  is  thus  seen  that  for  any  airscrew  it  is  possible  to  draw 
-curves  in  which  thrust,  torque,  and  efficiency  are  plotted  against 
the  ratio  V/N  D.  These  quantities  may  be  determined  experi- 
mentally for  a  number  of  similar  types  of  airscrews  in  which  the 
ratio  pitch/diameter  is  different,  and  from  the  experimental 
results  so  obtained  the  required  curves  can  be  plotted.  The 
efficiency  curve  for  each  airscrew  is  then  plotted  on  the  same 
sheet,  and  an  envelope  of  all  these  curves  is  drawn.  Each  point 
on  this  envelope  corresponds  to  a  particular  pitch  ratio  member 
of  the  series,  and  can  therefore  be  applied  to  the  design  of  an 
airscrew  which  is  required  to  fulfil  certain  given  conditions.  For 
example,  if  an  airscrew  of  this  type  is  required  of  diameter  D, 
with  maximum  efficiency  at  a  certain  definite  forward  velocity 
V,  corresponding,  say,  to  top  speed  or  best  climbing  speed,  and 
to  have  a  rotational  speed  of  N  revolutions  per  second,  the  ratio 
V/N  D  is  easily  calculated,  and  from  the  point  on  the  envelope 
of  the  efficiency  curve  corresponding  to  this  value,  the  correct 
pitch  ratio  can  at  once  be  read  off. 


DESIGN    OF   THE   AIRSCREW  289 

This  principle  can  be  extended  further  in  order  to  find  the 
best  blade  width  ratio  for  the  required  conditions.  A  number  of 
airscrews  having  the  correct  pitch  ratio  may  be  constructed  with 
varying  blade  width  ratios,  and  from  the  experimental  results  a 
further  series  of  curves  can  be  drawn,  each  corresponding  to  a 
particular  blade  wfclth  ratio.  The  envelope  of  these  curves  will 
enable  the  best  value  of  the  blade  width  ratio  for  the  particular 
conditions  under  which  the  airscrew  is  to  work  to  be  read  off. 

In  cases  where  it  is  possible  to  carry  out  tests  upon  model 
airscrews,  this  method  leads  to  very  good  results,  and  is  much 
more  reliable  than  the  method  of  calculation.  It  is  probable, 
however,  that  a  combination  of  the  two  methods  will  form  the 
final  basis  for  airscrew  design,  the  experimental  results  being 
used  to  give  the  necessary  correction  factors  which  the  purely 
theoretical  method  requires. 

Tractive  Power  developed  at  the  Airscrew. — The 
tractive  power  developed  by  an  airscrew  (P)  was  given  in 
Formula  70,  Chapter  VI.,  namely 


-[-(in— 


The  expression  (V/N/)2  is  the  slip-stream  factor,  and  it  will  be 
observed  that  when  the  product  N/  is  equal  to  the  forward 
speed  of  the  aeroplane  there  will  be  no  power  developed  by  the 
engine  save  that  required  to  overcome  friction. 

Again,  when  the  velocity  is  zero  —  that  is,  when  the  machine 
is  standing  —  the  power  developed  reduces  to  the  expression 

P  =  k  N3  D5 

The  constant  k  depends  upon  the  construction  of  the  airscrew, 
but  it  can  be  determined  experimentally  by  flying  the  machine 
and  noting  the  power  P  required  at  a  certain  definite  speed. 
This  for  horizontal  flight  at  speed  V  is  given  by  the  expression 

£  A  V3  Kx 


550 

where  Kx  is  the  drag  of  the  machine,  A  the  wing  area,  and  p  the 
density  of  air  per  cubic  foot. 

Naturally  the  efficiency  of  the  airscrew  varies  considerably 
under  different  conditions,  owing  to  the  variation  in  its  effective 
pitch.  It  has  its  maximum  efficiency  when  its  effective  pitch 
is  largest  —  that  is,  when  the  machine  is  travelling  fast  ;  and  its 

u 


2QO  AEROPLANE    DESIGN 

minimum  efficiency  when  the  effective  pitch  is  smallest — that  is, 
when  the  machine  is  climbing. 

Design  of  an  Airscrew  by  the  Blade  Element  Theory. 
— It  is  customary  to  commence  from  the  following  data,  which 
have  already  been  fixed  by  outside  considerations,  namely  : 

1.  The  horizontal  velocity  of  the  machine  V. 

2.  The  speed  of  the  airscrew  in  revolutions  per  second  N. 

3.  The  diameter  of  the  airscrew  D,  which  is  usually  fixed  by 

the  question  of  ground  clearance,  and  which  should  be 
as  large  as  the  machine  under  construction  will  permit, 
so  that  tip  velocity  does  not  exceed  1000  f.p.s. 

4.  The  B.H.P.  available  from  the  engine. 

5.  The  aerodynamical  properties  of  the  aerofoil  sections  it  is 

proposed  to  employ. 

It  is  intended  to  design  a  four-bladed  airscrew  of  10  feet 
diameter,  with  a  speed  of  1000  r.p.m.  The  aeroplane  is  fitted 
with  a  375  h.p.  engine,  and  is  required  to  do  130  m.p.h.  at  an 
altitude  of  10,000  feet.  It  will  be  assumed  that  the  engine 
power  diminishes  with  atmospheric  pressure,  the  pressure  at 
10,000  feet  being  70%  of  that  at  ground  level,  and  the  density 
at  that  altitude  being  72%  of  that  at  ground  level. 

The  aerofoil  characteristics  will  be  those  taken  from  Fig.  214, 
and  the  blade  proportions  will  be  taken  from  Fig.  216.  It  is 
first  necessary  to  determine  the  angle  A  for  each  section,  from 
the  relationship 

tan  A  =  — -^—       See  Fig.  213 

V  =  130  m.p.h.  =  190*8  f.p.s. 
N  =  1000/60       =     16*67 
tan  A  = 


from  which  expression  the  values  of  A  can    be  tabulated   as 
below  : 

Section  ......         A  B  c  D 

Radius  r  feet    ...        1*25       ...       175  ...       2*25       »,.       275 

Tan  A   ...         ...       1*46       ...       1*04  ...       0*81        ...       0*664 

A  55°36'      ...      46*87'  ...        39°        ...       33°35* 


DESIGN   OF   THE   AIRSCREW 


Section  ... 
Radius  r  feet 
Tan  A   ... 
A 


0-561 

29°i8' 


F 

375 
0-486 

25°55' 


0-429 
22°I3' 


291 
H 

475 
0-384 

21° 


The  blade  width  ratios  £/^max  and  the  aerofoil  characteristics 
are  now  taken  from  Figs.  216  and  214,  remembering  that  the 
latter  correspond  to  the  angle  of  attack  of  3°. 

The  evaluation  of  the  torque  and  the  thrust  can  now  be 
proceeded  with,  using  the  relations  already  established  in  this 
chapter,  namely,  formulae  83,  84. 


FIG.  217. — Torque  Curve  for  Airscrew. 


Torque  =  4  x  -00237  x  -72  x  190*8  x  190*8 


/         /V        /      L/K*\3    b    sin  A  +  0) 

X    £max    /      Ky   A  /    I    +   (   ~    )    T  ----  \    9    .  'Y~  r  . 

J  V  \KyJ  b^      sin2  A 

o 

Thrust  =  4  x  -00237  x  -72  x  190*8  x  190*8 

,         fSK  ~ 

x  ^max  /    K 
J 


.   9  . 
sm2A 


The  determination  of  these  integrals  is  best  effected  in 
practice  by  adopting  the  tabular  method  of  procedure  as  shown 
on  next  page. 


292 


AEROPLANE  DESIGN 


to 

OO 
O 

b 


co 


to 

00 


to 

10      M 


ON    OO     "3- 
10    OO     to 

Tj-     00      W 


to 

TT     co 

CN     rO 


O    vO    O 

O    ^O    ON 

to   oo   M 


CO     "^     <* 

o^   to    co 
co   to   co 


ON 


to 

to    r-*.  M  to  CO 

tO     ON,  M  CO  O 

b  b  b  b 


oo   o 


to    o 

Tf      ON 

b 


r>-  ON  N 

c^  O  ° 

r3  .  to 

o  o 


M    co 

O       M 

t>*  t^* 


CO 


to    o 

CO    CO 

b 


O       M        IO 


!>. 

oo 


CO    M 

to   to 


M      O     CO 

b   b   b 


to   r^  M  M  oo 

1-1     TJ-  N  CO  co 

ON  co  vO  O 

t>»  M 


to 
tfi 

OJ 

8  I 


t 

81 


+    + 


oj    U    01 


+ 
"> 


>>     X    >> 


DESIGN    OF   THE   AIRSCREW 


293 


These  values  are  next  plotted  against  the  radius  r  as  shown 
in  Figs.  217  and  218,  and  the  areas  enclosed  by  the  curves  very 
carefully  measured.  From  these  curves  it  was  found  that 


/ 


x      sin2  A 

cos  (A  + 
sin2  A 


dr  =  6-91 

dr  =  3-17 


hence  the  torque  required  to  drive  the  airscrew 

=  4  x  "00237  x  '72  x  190^8  x  190*8  x  6-9i  x  £ma5 
but  the  torque  available  from  the  engine 

_  70  x  375  x  55° 


2  7T    X 


1000 

60 


=  1375  Ibs.  ft. 
Equating  these  values 

Anax   =    1375/1720 

=  0*8  feet  =  9-6  inches 


FIG.  218. — Thrust  Curve  for  Airscrew. 

The  maximum  blade  width  having  thus  been  determined,  the 
dimensions  of  each  section  follow  at  once  from  the  third  and 
fourth  lines  of  table  on  page  292,  namely  : 


294  AEROPLANE   DESIGN 

Section A          B         c          D          E          F         G          H 

Blade  width — ins.      6'8i      7-69     8-64     9-36     9*6       9-31     8'o6     5*76 
Thickness — ins....      2-18     177     1*43     ri2     0*88     0-76     0*65     0*49 

The  thrust  of  the  airscrew 

=  4  x  '00237  x  72  x   i9o'S  x  190*8  x  o'8  x  3*17 
=  630  Ibs. 

Therefore  the  efficiency 

630  x  190*8 

""•^"375 

=  83-57. 

In  practice  it  is  found  that  the  efficiency  of  an  airscrew  is 
generally  slightly  higher  than  its  calculated  value ;  hence  it  is 
probable  that  this  figure  would  be  more  than  realised  if  tested 
under  the  conditions  assumed. 

The  general  lay-out  of  the  airscrew  can  now  be  developed  as 
shown  in  Fig.  219.  Each  section  must  be  drawn  in  its  correct 
position  along  the  blade  and  with  the  required  angle,  A  +  3°,  to 
the  axis  of  the  blade. 

The  following  points  should  be  observed  when  sketching  the 
aerofoil  sections  : — 

(a)  The  centre  of  area  of  the  sections  should  lie  on  the  blade 

axis. 

(b)  The  respective  positions  of  the  centre  of  pressure  of  the 

sections  should  be  arranged  about  the  blade  axis  so 
as  to  eliminate  as  far  as  possible  all  twist  upon  the 
blade.  For  this  reason  a  symmetrical  blade  is  unsuit- 
able, because  the  centres  of  pressure  in  this  case  would 
all  lie  on  one  side  of  the  centre  line  of  the  blade. 
By  adopting  some  such  shape  as  that  shown,  this 
unbalanced  effect  is  avoided. 

(c)  Sections  near  the  boss  of  the  airscrew  are  designed  chiefly 

from  considerations  of  strength,  and  the  adoption  of  a 
convex  instead  of  a  flat  face  is  a  help  in  this  direction, 
while  the  aerodynamical  loss  resulting  from  such  altera- 
tions at  these  sections  is  practically  negligible. 

The  contour  lines  of  the  blade  can  now  be  constructed.  This 
is  an  operation  which  demands  great  skill,  and  depends  for  its 
success  principally  upon  the  experience  of  the  designer.  Indeed, 
it  may  be  said  that  after  the  design  of  a  few  successful  airscrews 


DESIGN    OF   THE   AIRSCREW 


295 


an  airscrew  designer  will  no  longer  need  aerodynamical  data 
to  assist  him,  but  will  be  able  to  produce  an  efficient  airscrew 
merely  by  '  eye.' 

In  normal  flight  the  'slip'  of  the  airscrew  may  be  somewhat 
greater  than  that  corresponding  to  maximum  efficiency,  in  which 
case  small  variations  in  the  rotational  speed  will  be  accompanied 
by  appreciable  variations  in  the  value  of  the  thrust.  By  adjusting 
the  torque  of  the  engine,  allowance  can  be  made  for  any  small 
discrepancy  between  the  calculated  and  the  actual  behaviour  of 
the  airscrew. 


PLAN    OF    BLADE 
FIG.  219. — Lay-out  of  an  Airscrew. 


HI 


Stresses    in    Airscrew    Blades.  —  An    airscrew   blade   is 
generally  subjected  to  the  following  forces  : — 

1.  A  tension  due  to  centrifugal  force. 

2.  A  bending  moment. 

3.  A  twisting  moment. 

It  is  therefore  obvious  that  an  accurate  calculation  of  the 
combined  stresses  at  any  point  along  the  blade  is  a  matter  of 


296  AEROPLANE    DESIGN 

considerable  difficulty.  We  can,  however,  obtain  satisfactory 
results  by  considering  each  stress  separately.  In  a  well-designed 
airscrew  the  stresses  due  to  twist  will  be  quite  small,  since 
particular  care  will  have  been  taken  in  the  design  to  eliminate 
all  twist  as  explained  previously.  The  stresses  due  to  centri- 
fugal force  and  bending  moment  may  be  determined  as  follows  : 
Let  Fig.  220  represent  the  airscrew  blade,  and  let  'a'  be  the 
cross-sectional  area  of  a  section  of  the  blade  distant  '  x'  from 


FIG.  220.  FIG.  221. 

the  centre.    Then  the  centrifugal  force  set  up  by  a  small  element 
of  the  blade  at  this  distance 


weight  of  element  x  (velocity) 


Let  iv  be  weight  in  Ibs.  of  a  cubic  foot  of  the  material  of  which 
airscrew  is  made 

Then  volume  of  element   =  a  .  dx 

weight  of  element     =  w  a  .dx  Ibs. 
velocity  of  element  =  2  ?r  n  x  feet  per  second, 
hence  centrifugal  force  due  to  element 
_  w  a  .  d  x     4  7T2  «2  #2 

g  x 

The  stress  at  any  section  L  L1  of  cross-sectional  '  a  ' 


•f 


,      4  TT*  n-  w    . 
f  =  z    — . —    i       ax.d  x 
ga        ' 


The  value  of  the  integral  can  best  be  determined  graphically 
by  taking  values  of  the  product  a  x  along  the  blade  and  plotting 
them  on  an  ( x'  base.  The  area  of  the  curve  thus  obtained  will 
enable  the  stresses  due  to  centrifugal  force  to  be  determined 
with  considerable  accuracy.  A  simpler  but  not  so  accurate  a 
method  is  to  assume  the  blade  of  constant  section  over  a  certain 
distance,  and  to  treat  each  such  length  separately  by  determining 
its  weight  and  mean  distance  from  the  centre  of  rotation. 

Adopting  this  method,  the  stresses  due  to  centrifugal  force  in 
the  airscrew  just  designed  are  obtained  by  tabulation  as  shown 


FIG.  225. — Appearance  of  Airscrew  Laminations  before  shaping. 


Reproduced  by  courtesy  of  Messrs.  Oddy,  Ltd. 

FIG.  228. — Finished  Airscrew. 


Facing  page  296. 


DESIGN    OF   THE    AIRSCREW 


297 


below.  The  area  of  each  section  should  be  determined  by 
graphical  summation,  Simpson's  rule,  or  by  the  use  of  a  plani- 
meter.  The  weight  of  a  cubic  foot  of  mahogany  is  taken  as 
35  Ibs. 

TABLE  XLIII. — STRESSES  DUE  TO  CENTRIFUGAL  FORCE. 
Section ...         ...          A          B         c          D 

8-24     6-98 
49-4     41-9 
767      794 


Area  sq.  ins. 
Volume  cu.  ins. 
Centrifugal  force 

S  C    ... 

Stress  =  ~r~ 


A    B 

9'94  9'o< 
59'6  54'3 

5*4  655 
5202  4688  4033  3266 

524  519   490   469 


E 
5^4 

33'8 
758 
2472 

438 


F      G  H 

4*72  3*49  i'88 

28*35  20'95  11*28 

732  613  369 

1714  982  369 

364   282  196 


Rad.us  (if) 


1 

1.00 

i. 


r 

f! 


FIG.  222. — S.  F.  and  B.  M.  Diagrams  for  Airscrew. 

Stresses  due  to  Bending. — The  stresses  in  the  blade  due 
to  bending  are  set  up  by  the  air  pressure  exerted  upon  each 
element  of  the  blade.  Consider  a  section  of  the  blade  such  as  is 
shown  in  Fig.  221.  The  maximum  tensile  and  compressive 


298  AEROPLANE    DESIGN 

stresses  will  occur  in  the  outer  layers  of  the  material,  and  to  find 
their  values  we  require  to  know  the  bending  moment  at  the 
section  considered.  The  value  of  this  bending  moment  is 
determined  by  drawing  the  load  grading  curve.  The  ordinates 
of  this  curve  are  obtained  from  the  thrust  grading  curve  by 
dividing  the  thrust  at  each  section  by  cos  (A  +  0).  Since  this  is 
a  mere  ratio  the  thrust  grading  curve  can  evidently  be  used 
with  a  different  vertical  scale.  The  curve  of  shear  force  over  the 
blade  follows  directly  from  the  load  grading  curve  by  graphic  or 
tabular  integration,  whichever  is  preferred.  Similarly  integration 
of  the  shear  force  curve  gives  the  bending  moment  curve.  This 
work  is  quite  straightforward,  but  if  graphical  integration  is 
used  care  must  be  taken  to  see  that  the  correct  scales  are 
obtained.  Fig.  222  (a be)  shows  these  curves  for  the  airscrew 
under  consideration. 

The  bending  moment  at  each  section  is  then  read  off  from 
the  curve,  and  the  stresses  obtained  from  Formula  51. 

The  moment  of  inertia  of  the  sections  and  their  centre  of 
gravity  can  be  readily  determined  by  the  use  of  the  graphical 
method  outlined  for  a  streamline  strut  in  Chapter  IV. 

The  stresses  due  to  bending  are  tabulated  in  Table  XLIV. 
below. 

TABLE  XLIV. — STRESSES  DUE  TO  BENDING. 

Section        ...A          B          c          D          E  F         G  H 

I/yc  in.8        ...       2*46      1*83      i'34      0*89      0^565    o'4i  0^26  0*105 

I/Xt  in.3        ...      3*70      2*75      2*02       i '34      0*85      o'6i4  0*39  o'i6 
B.M.  Ibs.  ft. ...       365       286       214       146         87         40        15          4 

B.M.  Ibs.  in....     4390     3440     2570     1750     1040       480  180        48 

Compressive  Stress. 
Myc/I  Ibs.  per  sq.  in.       1790    1880    1920    1970    1840    1170    690    460 

Tensile  Stress. 
Mjt/I  Ibs.  per  sq.  in.       1190    1250    1270    1310    1225      780    460    300 

The  maximum  stresses  at  each  section  can  now  be  obtained 
by  adding  together  the  centrifugal  and  the  bending  moment 
stresses  of  Tables  XLIII.  and  XLIV. 

It  will  be  observed  that  the  tension  due  to  centrifugal  force 
will  diminish  the  compressive  stress  in  the  blade,  but  increase 
the  tensile  stress.  For  mahogany  or  walnut  the  maximum  per- 
missible working  stress  is  2000  Ibs.  per  square  inch.  The  stresses 
obtained  are  seen  to  be  well  within  this  figure. 


DESIGN    OF   THE  AIRSCREW  299 

TABLE  XLV. — MAXIMUM  STRESSES  IN  THE  AIRSCREW  BLADE. 

Section    A  B          c  D  E  F         G         H 

Compressive 

stress 1266     1361     1430     1501     1402       806     408     264 

Tensile  stress ...      1714     1769     1760     1779     1663     1144     742     496 

The  best  materials  at  present  available  for  the  construction 
of  airscrews  are  walnut  (black)  and  mahogany.  Walnut  is 
heavier  than  mahogany,  but  is  not  so  liable  to  warp  ;  on  the 
other  hand,  mahogany  takes  the  glue  better.  The  ultimate 
tensile  strength  of  either  material  is  about  4  tons  per  square 
inch,  so  that  a  working  stress  of  2000  Ibs.  per  square  inch  may 
be  considered  as  quite  satisfactory. 

The  method  of  building  up  an  airscrew  will  be  apparent  from 
a  study  of  Fig.  223.  The  thickness  of  the  laminae  varies  from 
|"  to  ii". 

Much  controversy  has  raged  round  the  question  of  the 
relative  merits  of  the  two-  and  the  four-bladed  airscrew.  The 
four-bladed  airscrew  is  probably  better  balanced  and  slightly 
more  efficient  than  the  two-bladed  variety,  but  the  latter  type  is 
easier  to  build,  and  can  also  be  made  stronger  at  the  boss. 

The  Construction  of  an  Airscrew. — As  already  stated, 
the  timber  most  frequently  used  for  the  construction  of  an 
airscrew  is  either  mahogany  or  walnut.  The  wood  should  be 
thoroughly  seasoned,  straight-grained,  and  quite  free  from  knots. 
The  use  of  curly-grained  timber  will  cause  the  blades  to  cast, 
and  should  therefore  be  avoided.  The  planks  from  which  the 
laminae  are  to  be  cut  should  be  stored  for  several  weeks  in  a 
room  where  the  temperature  and  atmospheric  conditions  are  the 
same  as  those  prevailing  in  the  workshop.  The  first  operation  is 
the  sawing  out  of  the  laminae.  The  dimensions  at  the  various 
sections  are  obtained  from  the  drawing.  A  template  giving  the 
shape  of  each  lamina  should  be  prepared  in  either  three-ply 
wood  or  in  aluminium  sheet.  A  margin  of  about  J"  in  the  case 
of  a  four-bladed  airscrew  and  of  about  £"  in  the  case  of  a  two- 
bladed  airscrew  should  be  allowed  all  round  to  compensate  for 
any  errors  in  gluing  in  position  or  change  of  position  due  to 
warping.  The  planks  should  then  be  marked  off  from  the 
templates,  the  grain  running  longitudinally  and  parallel  to  the 
flat  surface.  The  laminae  are  best  cut  out  with  a  band  saw  and 
then  planed  to  the  correct  thickness. 

In  the  case  of  the  four-bladed  screw  the   lamina   are  half 


3oo 


AEROPLANE    DESIGN 


lapped  at  the  centre,  as  shown  in  the  sketch,  Fig.  224.  The 
surfaces  which  receive  the  glue  should  be  '  toothed '  lengthwise 
along  the  blade.  The  laminae  are  then  supported  at  their  centre 
on  a  balance  and  the  heavier  ends  marked.  The  gluing  together 
of  the  laminae  can  now  be  commenced.  The  first  two  laminae 
are  thoroughly  warmed  by  placing  them  in  contact  with  a  hot 
plate,  and  then  their  adjacent  surfaces  are  quickly  covered  with 
best  Scotch,  French,  or  Lincoln  glue,  after  which  they  are  clamped 
together  in  their  correct  relative  positions  by  means  of  a  number 
of  hand-screw  clamps.  Clamping  should  be  commenced  at  the 
centre  of  the  block,  working  outwards  to  the  tip.  In  this  manner 
a  failure  of  the  glued  joints  at  the  boss  is  avoided.  It  is  also 
very  essential  that  the  temperature  of  the  glue  room  should  be 
maintained  at  a  uniform  temperature  of  about  70°  F.  throughout 
the  entire  process  of  gluing,  otherwise  an  opening  of  the  joints  is 


FIG.  223. 


FIG.  224. 


probable  after  the  airscrew  has  been  completed.  The  remaining 
laminae  are  then  glued  in  position  one  at  a  time,  a  period  of  at 
least  eight  hours  being  allowed  between  the  addition  of  each 
lamina.  The  process  of  warming  the  lamina  and  clamping  it 
down  on  to  the  block  is  exactly  similar  to  that  described  above 
for  the  first  two  laminae. 

In  order  that  the  position  of  each  lamina  relatively  to  the 
block  may  be  correct,  it  is  customary  to  locate  it  by  measure- 
ment from  the  preceding  one,  and  then  a  small  piece  of  wood  is 
glued  on  the  projecting  portion  of  the  lower  lamina,  and  the  side 
of  the  freshly  added  lamina  is  pressed  up  tight  against  this  small 
block.  Before  the  addition  of  each  lamina  the  block  is  checked 
for  balance  and  then  the  light  end  is  balanced  up  by  placing  the 
heavier  end  of  the  next  lamina  upon  it.  In  this  manner 
the  block  is  comparatively  well  balanced  at  the  completion 
of  the  gluing-together  stage.  After  gluing,  a  number  of  small 
pegs  are  driven  into  the  blades  at  positions  which  have  been 


DESIGN    OF   THE   AIRSCREW 


301 


indicated  upon  the  drawings.  They  should  be  a  moderate 
driving  fit,  and  glued  into  position.  The  boring  of  the  hole  in 
the  boss  is  the  next  operation.  This  is  best  performed  upon 
a  boring  machine,  the  cutter  being  run  at  a  high  speed  in 
order  to  obtain  accuracy.  The  block  is  then  set  aside  for  several 
days  in  a  room  the  temperature  cf  which  is  exactly  the  same  as 
that  prevailing  in  the  glue  room.  During  this  period  the 
tendency  of  the  blades  to  cast  or  warp  will  be  taken  up.  Fig. 
225  shows  a  4-bladed  airscrew  at  this  stage  of  construction. 

The  '  roughing-out'  stage  is  now  commenced,  and  the  blades 
are  shaped  down  to  within  about  J"  of  their  final  dimensions.  A 
further  period  of  several  days  is  then  allowed  for  the  timber  to 
take  up  any  change  of  state.  In  this  manner  a  more  accurate 
and  more  permanent  contour  is  finally  obtained.  Lastly,  the 
final  shaping  of  the  airscrew  is  proceeded  with.  The  correct , 
shape  and  angle  of  the  blade  sections  are  obtained  by  the  use  of 


FIG.  226. — Template  for  checking  Airscrew  Section. 

steel  or  aluminium  templates  such  as  are  shown  in  Fig.  226. 
The  balance  of  the  airscrew  should  be  frequently  tested  during 
this  latter  process  and  more  material  removed  from  the  heavier 
blades.  The  blade  surfaces  are  finally  smoothed  up  by  means  of 
glass-paper  and  the  airscrew  should  now  be  almost  perfectly 
balanced.  One  type  of  balance  for  testing  airscrews  is  shown  in 
Fig.  227.  A  thin  steel  tube  is  passed  through  the  airscrew 
hub,  and  the  airscrew  is  then  lifted  on  to  the  balance,  the  outer 
ends  of  the  tube  resting  on  two  knife-edged  plates.  Another 
method  is  to  support  the  tube  inside  roller  bearings  carried  on 
a  wall  bracket.  The  remaining  operations  are 

(a)  The  drilling  of  the  bolt  holes  through  which  pass  the 

bolts  which  attach  the  airscrew  to  the  steel  boss,  which 
in  turn  is  serrated  and  fits  on  to  a  correspondingly 
serrated  shaft  attached  to  the  engine  shaft. 

(b)  The  final  varnishing  of  the  airscrew  in  order  that  it  may 

withstand  climatic  conditions. 


102 


AEROPLANE    DESIGN 


The  first  of  these  operations  necessitates  the  use  of  a  drilling 
jig  for  which  a  standard  airscrew  boss  can  be  used  ;  while  for  the 
second,  two  or  three  coats  of  good  boat  varnish  with  an  oil  base 
should  be  used.  The  final  balance  of  the  airscrew  is  effected  by 
adding  extra  varnish  to  the  lighter  blades.  A  completed 
airscrew  is  shown  in  Fig.  228. 

The  practice  of  adding  brass  tips  to  the  airscrew  blades  was 


FIG.  227. — Testing  the  Balance  of  an  Airscrew. 


largely  adopted  during  the  war.  These  tips  are  bent  to  the 
correct  shape  on  a  former,  and  then  riveted  to  the  blades  by 
means  of  copper  rivets.  They  serve  as  a  protection  to  the  outer 
leading  edges  of  the  airscrew,  but  greatly  increase  the  stresses  at 
the  roots  of  the  blades  due  to  centrifugal  force.  The  sheathing 
of  the  blades  with  fabric  has  also  been  largely  adopted. 


CHAPTER   X. 
STABILITY. 

Definition. — The  stability  of  an  aeroplane  considered  from 
the  most  general  point  of  view  would  involve  a  discussion  of  all 
those  qualities  which  enable  a  machine  to  be  flown  in  safety 
under  all  the  varying  conditions  likely  to  be  met  with  in  flight 
in  all  weathers. 

The  stability  of  an  aeroplane  as  studied  in  this  chapter  will 
be  considered  from  the  more  limited  standpoint  of  the  following 
definition  :  '  If  a  body  be  moving  in  a  uniform  manner  relative 
to  the  surrounding  medium,  then  the  motion  is  said  to  be 
stable,  if  when  any  small  disturbance  takes  place  in  the 
medium,  the  forces  and  reactions  set  up  in  the  body  tend  to 
restore  the  body  to  its  original  state  of  motion  ;  while  if  the 
forces  due  to  a  small  initial  disturbance  tend  to  produce  a* 
further  departure  from  the  original  state  of  motion,  then  the 
motion  is  said  to  be  unstable.' 

Applying  this  definition  to  an  aeroplane,  it  is  seen  that  a 
machine  will  be  inherently  stable  if  after  a  sudden  dis- 
turbance in  its  flight  path  it  is  able  to  regain  correct  flying 
attitude  without  any  assistance  on  the  part  of  the  pilot. 

For  an  aeroplane  to  be  completely  stable  it  must  possess 
both  statical  and  dynamical  stability.  An  aeroplane  is  stati- 
cally stable  if  righting  moments  are  called  into  play  which 
tend  to  bring  the  machine  back  to  its  normal  flying  attitude  if 
deviated  therefrom  temporarily.  These  righting  moments  will, 
however,  set  up  oscillations,  and  the  machine  will  be  dynamically 
stable  only  if  these  oscillations  diminish  with  time  and  ulti- 
mately die  out,  leaving  the  machine  in  its  normal  flight  attitude. 
It  is  therefore  essential  to  establish  statical  stability  before 
making  an  investigation  of  dynamical  stability. 

The  question  of  stability  is  closely  inter-connected  with  the 
question  of  controllability.  A  machine  possessing  a  large 
amount  of  inherent  stability  is  sometimes  difficult  to  control,  or 
in  the  words  of  the  pilot,  is  said  to  be  '  heavy  on  the  control.'  It 
is  generally  necessary  to  make  a  compromise  between  the  two 
factors.  For  fighting  purposes  manoeuvrability  is  of  the  utmost 
importance,  and  it  is  essential  that  a  war  machine  should  answer 
very  rapidly  to  its  controls,  and  consequently  the  question  of 


304  AEROPLANE    DESIGN 

inherent  stability  is  not  of  such  vital  importance  as  in  the 
case  of  the  commercial  machine.  Reference  to  the  particulars 
given  in  Chapter  XIV.  with  regard  to  the  Bristol  Fighter  and 
the  S.E.  5  illustrates  that  fighting  machines  have  been  designed 
possessing  a  large  degree  of  both  inherent  stability  and  ma- 
noeuvrability. It  will  be  readily  appreciated  that  in  the  case  of 
long  distance  flights  an  aeroplane  which  continually  tends  to 
depart  from  the  normal  flight  path,  owing  to  minor  disturbances, 
requires  constant  attention  on  the  part  of  the  pilot,  and  imposes 
upon  him  a  very  severe  strain,  which  it  is  both  possible  and 
desirable  to  avoid. 

The  mathematical  theory  of  stability,  with  respect  to  an 
aeroplane  in  the  restricted  sense  of  the  above  definition,  has 
been  developed  principally  by  Lanchester*  and  Bryan.f  The 
application  of  Bryan's  theoretical  results  to  a  particular  machine 
was  very  ably  carried  out  by  Bairstow,*  and  much  of  the  sub- 
sequent matter  is  based  upon  his  work. 

The  theory  is  very  complex  and  those  desiring  a  fuller 
treatment  of  the  subject  should  consult  the  references  given 
below.  Our  aim  in  this  chapter  is  to  outline  the  theory  and 
to  show  its  application  to  the  results  of  tests  upon  models, 
and  then  to  indicate  the  method  whereby  the  stability  of  a 
completed  machine  may  be  predicted  from  these  wind  channel 
tests. 

The  investigation  of  stability  can  be  summarised  as  under  : — 

Summary  of  Procedure  : 

A.  Theoretical  determination  of  the  equations  of  motion  by 
mathematical  reasoning  in  terms  — 

(i.)  Of  the  velocities  of  the  C.G.  of  the  machine  along 

the  axes  of  reference  ; 
(ii.)  Of  the  angular  velocities  of  the  machine  about  the 

same  axes. 

B.  These  expressions  contain  a  number  of  constants  termed 
Derivatives,  which  can  be  divided  into  two  classes— 

(i.)  Resistance  Derivatives  which  depend   merely 
on  the  shape  and  size  of  the  machine,  and  not  on 
its  motion ; 
(ii.)  Rotary    Derivatives   which    depend   upon    the 

motion  of  the  machine. 

Both  classes  of  derivatives  can  be  determined   analyti- 
cally, and  also  by  means  of  model  tests. 

•*  Aerodonetics  (Constable  &  Co.).     t  Stability  in  Aviation  (Macmillan). 
%  N.  P.  L.  Report ',  1912-1913. 


STABILITY 


3°5 


C.  Substitution  of  the  values  obtained  for  the  derivatives  in 
the  general  equations  of  motion  developed  under  A  leads 
to  a  solution  in  many  important  cases,  and  consequently 
the  nature  of  the  motion  can  be  investigated. 

D.  The  investigation  of  the  small  oscillations  occurring  about 
the  steady  motion  of  an  aeroplane  leads  to  a  classifica- 
tion into  two  groups,  each  determined  by  three  equations 
of  motion.     These  groups  are  : 

(i.)  The  group  representing  motion  in  a  vertical  plane, 
and  determining  the  nature  of  the  longitudinal 
oscillations  upon  which  the  longitudinal  stability 
of  the  machine  depends. 

(ii.)  The  group  representing  motion  about  the  plane 
of  symmetry,  and  determining  the  nature  of  the 
rolling  and  yawing  oscillations  upon  which  the 
lateral  stability  of  the  machine  depends. 

Stability  Nomenclature. — The  N.P.L.  system  is  illustrated 
in  Fig.  229  and  tabulated  in  Table  XLVI. 

The  axis  O  x  corresponds  to  the  axis  of  drag  of  the  machine  in 

normal  flight. 

The  axis  O  z  corresponds  to  the  axis  of  lift. 
The  axis  Oy  is  perpendicular  to  the  plane  x  o  z. 
O  is  the  centre  of  gravity  of  the  machin  *. 

Rotation  about  the  axis  O  x  is  termed  ROLLING. 

Rotation  about  the  axis  Oy  is  termed  PITCHING. 

Rotation  about  the  axis  O  z  is  termed  YAWING. 

The  linear  velocities  in  the  directions  of  the  axes  are  denoted  by 

u,  v>  w  respectively,  and  the  angular  velocities  about  these  axes 

are  denoted  by/,  ^,  r  respectively. 

TABLE  XLVI. — STABILITY  NOMENCLATURE. 


Axis,  i            N^  rf 

UX1S. 

Name  of            S>'f'nbo1 
<°'~-             \   fof°cre. 

Name  of 
angle. 

Symbol 
for 
angle. 

Name  of 
moment. 

Symbol 
for 
moment. 

T 

O  x    Longitudinal 

Longitudinal      X 

Ro 

f 

Rolling 

Or    Lateral 

Lateral                Y 

Pitch 

8 

Pitching 

M 

O  z    Normal            Normal               Z 

i                         ' 

Yaw        i/, 

Yawing 

N 

The  signs  of  the  forces  are  positive  when  acting  along  the 
positive  directions  of  the  axes  indicated  by  arrows  in  Fig.  229; 
the  angles  and  moments  are  positive  when  turning  occurs  or 
tends  to  occur  from  Qy  to  O^  ;  Q  z  to  O.r ;  Ox  to  Oj. 

In    order  to  define  the   angular  position    of  an   aeroplane, 


3o6 


AEROPLANE   DESIGN 


Euler's  *  System  of  Moving  Axes'  is  adopted,  the  motion  of  the 
machine  being  referred  to  a  system  of  axes  fixed  in  the  machine 
itself.  If  the  motion  of  these  axes  be  known  with  reference  to 


FIG.  229. — Axes  of  Reference. 

any  set  of  axes  fixed  in  space,  then  the  motion  of  the  aeroplane 
is  completely  known.  In  Euler's  method  this  fixed  set  of  axes 
is  chosen  so  as  to  coincide  with  the  moving  body  axes  at  the 


FIG.  230. 


instant  under  consideration.  Hence  the  fixed  axes  are  con- 
tinually being  selected  and  discarded  during  motion.  This 
method  has  the  advantage  of  enabling  the  difficulties  of  referring 
the  motion  to  a  set  of  axes  fixed  in  space  to  be  avoided,  but 


STABILITY  307 

possesses  the  disadvantage  that  it  cannot  be  used  for  allowing 
the  flight  path  of  the  machine  to  be  continuously  traced  out. 

The  Equations  of  Motion.—  (a)  LINEAR  ACCELERATIONS. 
—  Let  OX,  O  Y,  o  Z  be  axes  fixed  in  the  machine  occupying 
positions  O  X,  O  Y,  O  Z,  and  O  X1  O  Vl  O  zl  at  successive  instants, 
as  in  Fig.  230. 

Let  u,  v,  w  be  the  velocities  of  the  machine  along  the  axes 
OX,  O  Y,  O  Z  ;  and  u  +  S  «,  v  +  §v,  w  -}-  §  w  the  velocities  of 
the  machine  along  the  axes  O  xlf  O  Ylt  O  zr  The  position  of  the 
axes  relative  to  each  other  is  obtained  by  first  rotating  the 
machine  through  an  angle  S  i/<  about  o  Z,  secondly  rotating  the 
machine  through  an  angle  S  0  about  the  new  axis  of  Y,  and 
lastly  by  rotating  the  machine  through  an  angle  of  8  <£  about  the 
new  axis  of  X. 

Increment  of  velocity  along  fixed  direction  o  x 

=  («  +  3  u}  cos  b  6  cos  b  4  +  (w  +  %  ^  sin  b  ft 

-  (v  +  &  v}  sin  b  ^  -  u 

=  u  +  ?>u  +  wb6  -  v  $  i//  -  u 

whence       neglecting  second  and  higher  orders  of  small  quantities. 
Acceleration  in  the  direction  o  x 


bt 


- 

dt          at         dt 

Similarly  the  increment  of  velocity  along  o  Y 

=  (v  +  8  v)  cos  b  0  cos  b  \L  +  (u  +  8  u)  sin  b 

-  (w  +  b  w)  sin  b  <p  -  v 

=  V-\-lv-\-U.'b-^   -   W  .  b  fy   —   V 

Acceleration  in  the  direction  o  Y 


It 


And  increment  in  velocity  along  o  z 

=  (w  +  b  w)  cos  b  6  cos  b  0  +  (v  +  b  v)  sin  b 

-  (u  +  £  u)  sin  b  0  —  w 

—  2V  +   b  W  +  V  .  b  (f)   —   U  .  b  0   —   W 

Acceleration  in  the  direction  o  z 

_3w  +  v.b<t)-ubO       dw  d<b  "       d 

-ft-  ~'^T  +  vJ7-u 


308  AEROPLANE   DESIGN 

Now  d^-  is  the  angular  velocity  of  machine  about  axis  O  .v  = 
d  t 


d± 
dt 


O  z  =  r 


Hence  the  acceleration  of  the  machine  along  the  three  axes 
of  reference  may  be  written 

Acceleration  along  O  x  =  —  +  w  /  -  v  r  =  X 


FIG.  231. — Angular  Accelerations. 

(^)  ANGULAR  ACCELERATIONS.— The  angular  velocities  of 
the  system  of  moving  axes  O  ^r,  O  y,  O  s,  about  any  instan- 
taneous position  are  represented  by/,  q,  r  respectively. 

Let  h^  h^  //3  represent  the  angular  velocities  of  the  machine 
about  these  axes. 

It  is  first  necessary  to  find  what  angular  acceleration,  it  any, 
is  entailed  in  the  superposing  of  the  above  angular  velocities. 


STABILITY 


3°9 


Consider  a  body  moving  in  the  plane  ZOX  (see  Fig.  232)  with 
an  angular  velocity  q  about  the  axis  o y,  and  rotating  with  an 
angular  velocity  h^  about  the  axis  o  xv 

At  a  time  '/'  the  axis  O  *\  makes  an  angle  qt  with  O;r. 
Mark  off  a  distance  O/along  axis  O^  to  represent  the  angular 
velocity  hv  Then  component  of  angular  velocity  about  axis 
O  x  =  og  =  /^  cos  q  t.  Also  component  of  angular  velocity 
about  axis  O  5  =  oe  =  h^  sin  q  t.  Differentiating  to  determine 
the  angular  accelerations, 

Angular  acceleration  about  O  x  =   -  q  h^  sin  q  t 
„  „  „      O  z  =        qh^  cos^/ 

Compounding  to  determine  the  resultant  angular  acceleration, 
Resultant  angular  acceleration  =   v  (q  k-jf  (sin2  q  t  +  cos2  q  t) 

=  •/*, 

This  acceleration  takes  place  about  an  axis  O  a,  which  rotates 
with  angular  velocity  q  about  Oj,  the  axis  Oa  always  being  at 
right  angles  to  Oy  and  O  ,tr 


FIG.  232. 


Applying  this  result  to  the  general  figure  shown  in  Fig.  231* 
it  is  seen  that  the  resultant  angular  acceleration  about  each  axis 
contains  three  terms,  two  being  due  to  the  angular  velocities 
about  the  other  two  axes,  and  the  third  being  due  to  the  rate  of 
change  of  its  own  angular  velocity.  The  angular  accelerations 
about  each  of  the  axes  can  consequently  be  written  down  in  the 


following  manner  : — 


Angular  acceleration  about  Ox 
„      Oy 


dt 


dt 


dt 


AEROPLANE    DESIGN 


r..'.- Considering  the  case  of  an  aeroplane  whose  position  in  space 
at  any  moment  is  indicated  by  the  axes  O  x,  O  y,  O  s,  making 
angles  of  9,  <f>,  i//,  with  the  fixed  axes  Q  xv  Oyv  O  z,  as  shown  in 
Fig.  233. 

Let  the  velocity  of  the  C.G.  of  the  machine  along  the  body 


FTG.  233. 

axes  be  «,  v,  and  w  respectively,  and  the  angular  velocity  of  the 
machine  about  these  axes  be  p,  q,  r. 

The  general  equations  of  motions  will  then  be 


m  (u  +  w  q  —  v  r)  =  m  X 
m  (v  +  u  r  -  wp)  =  m  Y 
m(w+vp  - 


Formula  87 


y/2  -  p  hz  +  r  hl  =  ;«  M 

where       u  =  -=—  ;  and  similarly  for  v,  etc. 
m  =  mass  of  the  aeroplane 

/&2=^B-rD-/F 
*k-rC-/B-fD-' 


STABILITY  311 

A  B  C  D  E  F  are  the  moments  and  products  of  inertia. 

In  the  general  problem  the  air  forces  X,  Y,  Z,  and  the  air 
moments  L,  M,  N,  are  functions  of  the  velocity  components, 
and  of  0,  ^,  and  ;//,  and  a  disturbance  from  the  normal  flying 
speed  and  attitude  causes  a  change  in  each  of  these  quantities. 
If  U  be  the  normal  flying  speed  and  the  disturbance  be  small, 
then  u,  v,  w,  /,  q,  r,  9,  0,  ;//  are  small  compared  with  U,  so  that 
we  can  write 

X  =  /(U,  K,  v,  wtpt  q,  r,  6,  0,  i/,), 
which  can  be  expanded  into  the  approximate  form 

X  =  u  Xu  +  v  Xv  +  w  Xw  +/  Xp  +  q  Xq  +  r  Xr  +  X0  +  g  sin  0 

which  is  a  linear  function  of  the  small  quantities  utvt  wyp,q,  r>  0. 
The  coefficients  of  these  small  quantities  are  the  derivatives, 
which  represent  physically  the  slope  of  the  curve  of  X  upon  a 
base  of  u,  v,  w,p\  q,  r  respectively.  In  a  similar  manner  we  have 

Y  =  u  Yu  +  v  Yv  +  w  Yw  +  /  Yp  +  q  Vq  +  r  Yr  +  Y0  -  g  cos  0  sin  0 
Z  =  u  Zu  +  v  Z  v  +  w  Zw  +  /  Zp  +  q  Zq  +  r  Zr  +  Z0  -  g  cos  0  cos  0       °° 
L  =  u  Lu  +  v  Lv  +  iv  Lw  +  p  Lp  +  q  Lq  +  r  \  ,r  +  L0 
M  =  «  Mu  +  v  Mv  +  ze/  Mw  -f  /  Mp  +  ^  Mq  +  r  Mr  +  M0 

N  =  «  Nu  +  v  Nv  +  w  Nw  +  /  Np  +  q  Nq+  rNr  +  N0 

Before  proceeding  to  form  the  equations  for  small  oscilla- 
tions, it  should  be  observed  that  from  considerations  of  the 
symmetry  of  the  aeroplane,  eighteen  of  the  derivatives  will  be 
zero.  For  this  reason  the  derivatives  X,  Z,  M  disappear  when 
the  suffix  is  v,p,  or  r,  and  the  derivatives  Y,  L,  N  disappear 
when  the  suffix  is  u,  ^v,  or  q. 

Separating  the  equations  of  steady  motion  from  those  for 
small  oscillations  by  writing  (U  +  u)  for  u,  (V  +  v}  for  v,  (0  +  01) 
for  0,  etc.,  and  omitting  those  derivatives  whose  value  is  zero, 
and  combining  formulae  87  and  88,  the  equations  become 


m[u  +  (W+  w)(Q+g)  -  (V  +  p)  (R  +  r)}  « 
X0  +^sin(0'  +  8)] 


m(v  +  (U  +  u)(R  +  r)  -  (W  +  a/)(P  +/)]  =  m{v  Yv  +/  Yp+  rYr+ 
Y0  -  ^cos(0'+  0)sin('+ 


«i[w  +  (V  +  »)(P  +/)  -  (U  + 

Z0  -  g  cos  (0'  +  0)  cos  (</>'  + 

p  A  -  ^  F  -  r  E  -  r  h.2  +  ^  //3  =  m  [v  Lv  +  /  Lp  +  r  Lr  +  L0] 
//  B  -  r  D  -  /  F  -  /  As  +  r  ^  =  m  [u  Mu  +  w  Mw  +  ?  Mq  +  M0] 
/•  C  -  p  E  -  q  D  -  ^  ^  +  /  h.2  =  m  [v  Nv  +  /  Np  +  r  Nr  +  N0] 


312  AEROPLANE    DESIGN 

By  limiting  the  conditions  to  those  occurring  in  steady  flight 
In  a  straight  line  in  the  plane  of  symmetry  .r  O  s,  this  plane  being 
vertical,  these  equations  can  be  still  further  simplified.  For  such 
conditions 

the  dash  attached  to  an  angle  being  used  to  denote  the  angles 
for  flight  under  such  conditions. 

The  .terms  such  as  X0,  Y0,  Z0,  &c.,  are  included  in  the  con- 
ditions of  steady  motion.  For  equilibrium  in  steady  flight  X,, 
and  Z0  are  balanced  by  the  thrust  of  the  airscrew  and  force  of 
gravity  respectively,  and  since  there  is  no  side  force  on  the 
machine  the  various  moments  are  zero.  For  steady  motion, 
therefore,  when  axis  of  machine  is  at  an  angle  9'  to  the  direction 
of  flight, 

X0  +  g  sin  6'  =  o  ;     Z0  -  g  cos  0'  =  o  ;     Y0  =  o ; 

L0  =  M0  =  N0  =  o;     9  =  0  =  o 

Hence,   neglecting  small    quantities    of  the    second    order,   the 
equations  of  small  oscillations  reduce  to 

«  +  W<7  =  uXu  +  wXw  +  </Xq  +  Qg  cos  6'  ' 

v  +  U  r  -  W/  -  v  Yv  +  /  Vp  +  r  Yr  -  $g  cos  ft' 
w  -  U  ?  =  Zu  +  w  Zw  +  q  Zq  +  tig  sin  0' 

p  A  -  /  E  =  m  [v  Lv  +  /  LP  4-  r  Lr] 

q  B  =  /;/  [u  Mu  +  w  Mw  +  q  Mq] 

r C  -  /  E  =  ;;/(>  Nv  +  /  Np  +  rNr] 

The  oscillations  being  small,  it  can  be  assumed  that  the 
displacements  are  proportional  to  £Xt,  so  that  the  rate  of  change 
of  each  of  the  quantities  u,  v,  w,p,  q,  r,  is  proportional  to 

X,  or  —  -  =   u  =  X  u  and  so  on. 
at 

Also  by  a  suitable  choice  of  axes  W  can  always  be  made 
zero,  and  the  generality  of  the  equations  is  not  affected  thereby. 

Further,  by  writing  the  moments  and  products  of  inertia, 
represented  by  A,  B,  etc.,  in  the  form  m  k^,  m  £B2,  etc.,  where 
X-A,  £„,  etc.,  represent  the  radii  of  gyration  about  the  respective 
axes,  it  is  possible  to  eliminate  the  mass  of  the  machine  from 
the  equations,  Formulae  89. 

The  resulting  equations  can  be  divided  into  two  groups 
representing  the  Longitudinal  and  the  Lateral  Oscillati  -ns- 
respectively,  and  are  best  expressed  in  the  form  of  t\vo  de- 
terminants, namely — 


Formulae  90. 


STABILITY 


i.  LONGITUDINAL  OSCILLATIONS. 

X  -  Xu     ,      -  Xw     ,  '  -  XXq  - 
-  Zu     ,  X  -  Zw     ,      -  X  (U  + 


-  £•  sin 


-  Mu   ,      -  M, 


X  (  -  Mq  +  X 


=  o 


Formula 


2.   LATERAL  OSCILLATIONS. 

X  -  Yv     ,       •  cos  0  -  X  Y 


-  Lv 

-  Nv 


X  (  -  Lp  +  X  / 
X  (  -  Np  -  X 


X  (U  -  Yr)  +  g  sin  0' 
-  X(Lr  +  X*E2) 


.........  ....  Formula  92.. 


Bryan  has  shown  that  the  solution  of  these  equations  can  be 
written  in  the  form 

AX4    +  B  X3    +  C  X2    +  D  X    +  E    =o 

Al  X4  +  B!  X3  +  Gj  X2  +  Dt  X  .+  ET  -  o      Formula  93, 

For  stability  the  quantity  A  must  be  negative  if  real,  or  have 
its  real  part  negative  if  it  is  complex,  in  which  cases  the 
amplitude  of  the  oscillations  diminish  with  time.  The  condition 
that  the  real  roots  and  the  real  parts  of  imaginary  roots  of 
Formula  93  may  be  negative,  is  that  the  coefficients  A,  B,  C, 
D,  E,  shall  each  be  positive,  and  also  that  the  quantity 
B  C  D  -  A  D'2  -  B2  E—  generally  known  as  Routh's  Discrimi- 
nant —  shall  be  positive.  In  this  manner  Bairstow  has  derived. 
the  following  values  for  the  coefficients  from  Formulae  91,  92. 


LONGITUDINAL  OSCILLATIONS. 


A  =  K1;- 


B  -   -     M 


c  -    zw    , 

U    +    Zq          +          Xu 

j            Q          '     *n~       ^>u       j       -**-w 

Mw    , 

Mq                                     Mu 

,        Mq                                  Zu          ,          Zw 

I)  m     -      Xu 

,         Xw         ,         Xq 

-  g     Mu    ,    -  sin  B' 

zu 

,         Zw         ,         U    +    Zq 

Mw    ,    cos  6 

Mu 

,          Mw       ,          Mq 

E  =   -  g    Xu 

,     Xw     ,     cos  B' 

Zu 

,     Zw      ,     s:n  0' 

M 

M           9 

.  Formulae 

3'4 


AEROPLANE   DESIGN 


A- 


LATERAL  OSCILLATIONS. 


c,= 


T  —  1?  2          _  A 

-'--'y    »          AA  >          A 

NA   2  A 

V     5  ^E  J  ** 

Yv  ,  Yp  ,      o 

T  I  T?  2 

•My    j  i^p    j  —  «:H 


i    N 


N 


p  » 


YY  , 


,    Yr-U 


D1  = 

YV,Y 

v 

3  >    x  r 

u 

Ly,L 

p  >  *-« 

Nv,Np,Nr       ' 

E!  =   -  g  cos  0 

LV   , 

Lr 

Nv  , 

Nr 

T  1?  2          T 

l^y  ,     —  "-A  )        *^P 

N  b  2        "NT 

**V  I          ^E  >       *•';! 


Lv  ,  -  KE2 

Nv  ,  -  Kc2 


N  N 


N 


sin  0' 


Lr 

Nr 


Nv, 


+  g  sin  6 


Formulae  95. 


The  application  of  these  formulae  to  the  investigation  of  the 
stability  of  an  aeroplane  appears  a  formidable  task,  but  it  will 
be  shown  subsequently  that  several  of  the  derivatives  included 
in  the  above  expressions  are  of  minor  importance  and  may  be 
neglected.  This  results  in  much  simpler  expressions. 

The  Resistance  and  Rotary  Derivatives Before  pro- 
ceeding to  the  solution  of  the  biquadratic  equations  it  is 
necessary  to  consider  the  manner  in  which  the  resistance 
•derivatives  depend  upon  the  dimensions  of  a  machine.  Simple 
mathematical  expressions  can  be  deduced  for  most  of  these 
•derivatives,  enabling  a  much  clearer  conception  to  be  formed  as 
to  their  dependence  upon  the  form  of  the  machine.  The  experi- 
mental value  of  the  derivatives  for  the  model  of  a  Bleriot 
monoplane  constructed  to  a  scale  of  one-twentieth  full  size,  its 
shape  and  leading  dimensions  being  shown  in  Fig.  234,  was 
carried  out  by  the  N.P.L.  The  model  experiments  were  carried 
out  at  a  speed  of  30  feet  per  second,  while  the  normal  speed  of 
the  prototype  was  65  m.p.h.  (95*4  f.p.s.).  The  weight  of  the 
actual  machine  was  1 800  Ibs. 

To  convert  the  model  results  to  the  full-size  machine  the 
following  conversion  factors  were  therefore  used  : — 


X    20" 


STABILITY 


Force  on  machine  =  force  on  model  x  (  £2-2  \ 

V  30    / 

=  4040  x  force  on  model 

Moment  on  aeroplane  =  moment  on  model  x  (  -2±Lf  1    x  2o3 

V   3°    / 
=  80800  x  moment  on  model 

It  should  be  noted  that  the  methods  to  be  adopted  in  the 
investigation  of  the  stability  of  any  machine  will  be  upon  similar 
lines  to  those  outlined  here  for  the  Bleriot  monoplane.  The 
various  derivatives  will  be  considered  in  turn  and  the  method  of 
their  determination  fully  explained. 


A.  Derivatives  affecting  Longitudinal  Stability. — Xu 
This  is  the  rate  of  change  of  horizontal  force  with 
forward  speed.  Let  the  forward  speed  of  the  machine 
increase  from  'U  to  U  +  u 

It  may  here  be  pointed  out  that  as  the  motion  of  the  aero- 
plane is  in  the  negative  direction  along  the  axis  of  X,  the 
sign  of  U  will  always  be  negative  in  actual  flight.  It  is  also 
convenient  to  have  an  expression  for  wind  velocity  relative  to 
the  aeroplane,  although  it  only  varies  from  the  velocity  of  the 
machine  in  its  sign.  For  this  purpose  we  shall  use  the  symbol 
'U,  which,  of  course,  is  connected  with  U  by  the  relation 
'U  =  -  U 


3i6 


AEROPLANE    DESIGN 


The  equilibrium  forces  other  than  those  due  to  the  airscrew 
vary  as  the  square  of  the  forward  velocity,  hence  the  horizontal 
force  or  drag  ;;/  X0  becomes 

m  x  /  ru  ~  frr  \  =  m^    (  i    -  2U\ 
Differentiating  this  expression  with  respect  to  u,  we  get 


whence 


~  2 


where  X0  is  the  drag  per  unit  mass. 


X  *i 


CVu, 


\ 


Chas 


-6*        -<**       -2°        0          2°         4* 
Angle  of   Pihch    6 


8° 


FIG.  235. — Forces  and  Moments  on  Model 
Bleriot-type  Monoplane. 

The  experimental  determination  of  X0  is  carried  out  as 
follows :  The  model  is  supported  in  the  wind  channel,  and 
measurements  are  made  of  the  longitudinal  force  X — that  is,  the 
force  along  the  airscrew  axis — for  varying  angles  of  incidence. 


STABILITY  317 

The  observations  made  upon  the  Bleriot  model  covered  a  range 
of  pitch  from  —  8°  to  -f  14°,  and  are  shown  graphically  in 
Fig.  235. 

The  value  of  X  when  the  angle  of  pitch  is  zero  is  the 
required  value  of  X0  From  Fig.  235  this  is  seen  to  be 
o-o62  Ibs.  for  the  Bleriot  monoplane,  and  therefore  it  will  be 
4040  x  "062  =  250  Ibs.  for  the  full-size  machine.  Consequently 

5°  *  32*2 

•*    — o 

—  95*4        IGOO 
=    -  0-0935 
Generally    Xu  may  be  expected    to    lie    between    —  0^05   and 


Xw    Variation    of    longitudinal    force    due    to    a 
normal  velocity  of  the  machine  relative  to  the  wind. 

The  effect  of  a  small  upward  velocity  of  the  machine  is  to 
reduce  the  angle  of  incidence  of  the  wings.  If  w  be  this  small 
normal  velocity,  then  the  reduced  angle  of  incidence 


This  variation  is  equivalent  to  a  small  angle  of  pitch  d9 
away  from  the  equilibrium  position,  and  in  the  limit  we  may 
write 


=  ~   /.<?.,  w 


j  -\r 

whence  since         Xw  =  —  (from  definition) 


j  ~Y" 

we  have  Xw  =  rrr-r^  where  dQ  is  in  radians 


or  =  sLL£  —  -  where  d  0  is  in  degrees 

U    d  6 

dX/dO  is  the  slope  of  a  curve  of  X  on  a  base  of  angles  of  pitch. 
and  when  this  curve  has  been  drawn  its  slope  where  6  is  zero 
may  be  ascertained. 

It  is  thus  seen  that  Xw  is  proportional  to  the  slope  of  the 
longitudinal  force  curve.  Referring  to  the  curves  for  the  model 
given  in  Fig.  235,  the  value  of  the  slope  of  the  curve  for  X  for 
zero  angle  of  pitch  is  —  '0035.  For  the  full-size  machine  we 
therefore  have 


—  =   -  4040  x  -0035  =    -  14-12 


3i8  AEROPLANE   DESIGN 

Xw   =     -  5l_5  -   x     -    14*12    =   OTC2 

-  95  4  x  56 

Note  56  =   —  —  =  mass  of  machine 

32-2 

Generally  Xw  may  be  expected  to  lie  between  o  and  '4. 

Zq  The  variation  of  longitudinal  force  due  to 
pitching.  This  derivative  cannot  be  traced  to  any  definite 
part  of  the  machine,  but  is  apparently  of  small  importance,  and 
may  be  neglected  in  the  stability  equations. 

Zu  The  rate  of  change  of  normal  force  with  for- 
ward velocity.  In  a  similar  manner  to  that  adopted  above 
for  Xu,  it  can  be  shown  that 


In   horizontal  flight  Zu  may  be  expected  to  vary  between 
—  1*3  and  —  0*4,  the  higher  value  corresponding  to  a  low  speed. 

Zw  The   variation   of  the  normal  force  due  to  a 
normal  velocity  of  the  machine  relative  to  the  wind. 

Exactly  as  in  the  case  of  Xw  it  can  be  shown  that 

z     _  57'3  dZ 

'  "         ~ 


The  value  otdZsjdB  is  obtained  by  measuring  the  air  forces 
on  the  model  normal  to  the  airscrew  for  varying  angles  of  pitch. 
Measurement  of  the  slope  of  the  curve  of  Z  for  zero  pitch  angle 
gives  the  required  value.  The  normal  force  does  not  differ 
much  from  the  lift  of  the  machine  for  the  usual  range  of  flying 
angles. 

For  the  Bleriot  model  the  value  of  dZ/dO  for  6  =  o,  as 
obtained  from  the  curve  shown  in  Fig.  235,  is  "055.  For  the 
full-size  machine 

—  =  4040  x  -055  =  222 

whence  Zw  =  -  iZJ!  -  x  222  =   -2*4^ 

-  95'4  x  56 

Zw  is  generally  found  to  vary  between  —  1*5  and  —  4.5. 

Zq  Variation  of  the  normal  force  with  pitching, 

The  value  of  this  derivative  is  not  important,  as  the  terms 
depending  upon  it  in  the  stability  equations  are  small.  It  can 
therefore  be  neglected. 


STABILITY  319 

Mu  The  rate  of  variation  of  pitching  moment 
with  variation  of  forward  speed.  Since  there  is  no 
pitching  moment  upon  the  machine  in  steady  flight  the  value 
of  this  derivative  is  zero. 

Mw  The  variation  of  pitching  moment  with  normal 
velocity.  Similarly  to  Xw  it  can  be  shown  that 


_ 
'  ^'U~      0 

being  the  slope  of  the  pitching  moment  curve  at  zero- 
angle  of  pitch.  In  order  to  determine  this  curve  the  model 
is  suspended  in  the  wind  channel  and  the  pitching  moment 
observed  for  various  angles  of  pitch.  The  curve  of  M  for  the 
model  is  shown  in  Fig.  235. 

From  this  curve  the  value  of  the  slope  for  zero  pitch  is 
found  to  be  —  -00255,  whence 

AT     _  57*3  x    ~  *OO255  x  80800 
ivivv  —  -  —  -  — 

-  95-4   x  56 

=    2'2I 

This  moment  is  principally  due  to  the  action  of  the  elevator 
and  tail  plane,  modified  by  the  couple  due  to  movement  of  the 
centre  of  pressure  of  the  main  planes  and  by  a  couple  due  to 
the  fin  action  of  the  body.  Generally  it  is  found  to  vary 
between  2  and  6  for  horizontal  flight. 

Mq  The  variation  of  pitching  moment  with 
pitching.  It  is  not  possible  to  develop  a  simple  expression 
for  this  derivative,  and  the  method  adopted  for  determining  its 
value  is  to  oscillate  a  model  in  the  wind  channel.  The  model 
is  supported  by  a  spindle  passing  through  its  centre  of  gravity 
and  by  means  of  a  spring  a  slight  angular  displacement  is  com- 
municated to  the  machine,  which  commences  to  oscillate  about 
the  position  of  equilibrium  corresponding  to  the  angle  of  attack. 
These  oscillations  are  recorded  photographically,  and  from  a 
comparison  of  the  damping  with  and  without  the  wind  the 
value  of  Mq  can  be  evaluated.  Its  value  is  affected  by  the  tail 
planes,  body,  and  main  planes,  and  for  the  average  size  of 
machines  will  vary  from  —  100  to  —  300.  For  the  Bleriot 
monoplane  Mq  was  found  to  be  —  175. 

B.  Derivatives  affecting  Lateral  Stability.  —  YY  The 
variation  of  lateral  force  with  side  slip.  This  deriva- 
tive is  almost  entirely  due  to  the  resistance  of  the  side  area  of 


320  AEROPLANE    DESIGN 

the  body   and   fin,  and  may  be   expressed  very  simply  in  the 

57.3  ^Y 


where  d-Y/difr  is  the  slope  of  the  lateral  force  curve  at  zero 
angle  of  yaw.  As  the  machine  side-slips,  the  direction  of  the 
wind  relative  to  it  no  longer  acts  along  the  axis  of  x,  but  has  a 
small  component  along  the  axis  of  y.  This  component  will 
set  up  a  lateral  force  on  the  machine  tending  to  make  it  yaw. 
The  magnitude  of  this  force  must  be  determined  by  direct 
"experiment,  and  then  the  value  of  Yv  can  be  calculated. 

The  experimental  method  is  to  support  the  model  in  the 
wind  tunnel  by  means  of  a  spindle  attached  to  the  balance  arm 
and  then  to  rotate  the  model  through  various  angles  of  yaw 
from  the  symmetrical  position,  the  angle  of  pitch  being  kept 
at  zero.  Proceeding  in  this  manner  the  lateral  force  Y  on  the 
Bleriot  model  was  determined,  the  results  being  shown  in 
Fig.  236.  It  will  be  seen  that  Y  is  negative,  thus  indicating 
that  its  tendency  is  to  oppose  side-slipping.  This  naturally 
is  the  general  case,  but  it  should  be  noted  that  the  lateral  force 
due  to  certain  parts,  particularly  the  struts,  increases  the  side- 
slipping. The  lateral  force  becomes  greater  and  greater  as  the 
side-slipping  increases,  an  effect  which  makes  for  safety. 

By  measuring  the  slope  of  the  curve  of  Y  at  the  origin,  the 
variation  of  lateral  force  per  decree  of  yaw  is  determined.  This 
is  found  to  be  —  '0025  for  the  Bleriot  model,  whence 

Yv  =   -   -  —  H-J  —  x  '0021;  x  4040 
95'4  x  56 

=   -  0*108 
Yv  may  be  expected  to  vary  between  —  0*1  to  —  0*4 

Lv  Variation  of  rolling  moment  due  to  side  slip. 

This  can  be  expressed  in  the  same  manner  as  Yv,  namely, 


where  d^Ljd^  is  the  slope  of  the  curve  of  rolling  moment  at 
zero  angle  of  yaw.  The  model  is  suspended  in  the  wind  channel 
and  the  rolling  moment  on  the  machine  for  various  angles  of 
yaw  is  observed.  The  results  for  the  Bleriot  model  are  shown 
in  Fig.  236.  The  slope  at  the  origin  is  seen  to  be  -0008,  whence 

Lv  =  —  ^-^  —  x  -0008  x  80800 
95'4  x  56 

=  070 
The  value  of  Lv  varies  from  0-4  to  5. 


STABILITY 


321 


It  is  possible  to  develop  a  mathematical  expression  for  the 
value  of  this  derivative  in  a  fairly  simple  manner,  and  as  it  is 
probable  that  mathematical  expressions  will  be  available  for  all 


FIG.  236. — Forces  and  Moments  on  Model  Bleriot-type  Monoplane. 


the  derivatives  in  the  near  future,  we  outline  below  the  necessary 
steps  in  developing  such  formulae  on  a  logical  basis. 

The  damping  of  the  rolling  moment  on  a  machine  depends 
almost  entirely  upon  the  wings  and  tail  plane.  Let  us  consider 
the  effect  of  each  in  turn. 

Y 


322  AEROPLANE    DESIGN 

Consider  the  wings  of  a  machine  as  shown  in  Fig.  237.  The 
dihedral  angle  is  /3  as  shown.  Suppose  that  the  machine  is 
moving  along  the  axis  of  x  with  a  velocity  U,  and  that  a  side 
gust  strikes  it  with  a  velocity  v.  Then  the  direction  of  the 
relative  wind  will  be  along  O  P.  The  angle  of  incidence  of  the 
right-hand  surface  will  be  increased  from  i  to  i  +  S  i  ;  while 
that  of  the  left-hand  surface  will  be  diminished  by  8  i.  From 
the  geometry  of  the  figure  it  will  be  seen  that 


This  alteration  in  the  angle  of  incidence  of  the  wings  will  set  up 
a  moment  on  the  machine  tending  to  turn  it  about  the  axis  of  x. 
Let  dY^y\di  be  the  slope  of  the  Lift  Incidence  curve  for  the 


FIG.  237. 

wing  section  used,  then  the  increase  of  lift  upon  any  element 
considered  is 


=    b  -  dy  •  . 

A'  di 

=  lb  -  dv  -  v.'V  •  /3  • 
g 

and  the  moment  of  the  element 

P7  7  '  f  T  T 

--  b  -  dy  -  v  -    U  •  /3 

o-  di 

o 

whence  Total  Moment 

d 


-  ft'.v.  fl.'V  • 

J    g 


=  \m  •  v  •    Lv 
whence,  for  wings  of  rectangular  plan  form 

L,  =  ±£-fi  •  'U  -   ^  • 
g  m  di 

-  ft  -  d-^ 


gm 


di 


STABILITY 


323 


In  a  similar  manner  Lv  due  to  the  tail 

O         /TT      -,,  d  KV' 

=    ^—17/3      .  .y  - 
gm  di 

where         /3  =  dihedral  of  tail 


Jt       7/ 

b  d 


~^  =  slope  of  lift/incidence  curve  for  tail 

b'  =  chord  of  tail 
d'  =  span  of  tail 

The  total  value  of  the  derivative  Lv  will  be  approximately  the  sum 
of  these  two  expressions. 


4°  8° 

Angle    of    Incidence 


FIG.  238. — Characteristics  of  Bleriot  Aerofoil. 

It  will  be  seen  that  the  value  is  directly  proportional  to  the 
dihedral  angle  of  the  planes,  and  since  the  '  end  effect '  causes 
a  variation  in  dK^jdi  at  the  wing  tips,  this  effect  must  be  taken 
into  account  if  a  strictly  accurate  result  is  to  be  obtained  by  the 
use  of  the  above  formulae. 

In  applying  these  formulae  to  the  case  of  the  Bleriot  machine, 


324 


AEROPLANE   DESIGN 


it  is  necessary  to  know  the  characteristics  of  the  wing  section 
employed.  These  are  shown  in  Fig.  238.  The  angle  of  inci- 
dence of  the  wings  throughout  the  test  was  6°,  the  dihedral 
angle  is  1*8° 

whence      Lv  =  °°4^  x  9^-4  x  r8  x  -045  x  ^-  x  [JL]    x  2o3 

56  12  \I2/ 

=    0'62 

The  experimental  value  of  Lv  was  07 

It  will  be  observed  that  the  span  of  the  wings  has  been  taken 
in  the  calculation  as  9*0"  instead  of  the  actual  97"  in  order  to 
allow  for  the  variation  in  chord  at  the  wing-tip  ;  also  that  no 
term  due  to  the  tail  plane  has  been  added,  owing  to  the  fact  that 
there  is  no  dihedral  angle  on  the  tail.  The  body  and  the  fin 
would  have  a  slight  effect  upon  the  value  of  this  derivative,  and 
would  account  for  the  discrepancy  shown. 

NY  The  variation  of  Yawing  Moment  due  to 
Side-slip. — This  derivative  may  be  determined  by  suspending 
the  model  in  the  wind  channel  at  zero  angle  of  pitch  and 
measuring  the  variation  in  yawing  moment  over  a  range  of 
angles  of  yaw.  From  the  resultant  curve  the  value  of  Nv  may 
be  calculated  from  the  relationship 

The  curve  of  yawing  moment  for  the  Bleriot  model  is 
shown  in  Fig.  236,  from  which  curve  the  value  of  the  slope  for 
zero  angle  of  yaw  is  found  to  be  —  "0005,  whence 

Nv  =  — 57__o. —     x  (  -  '0005   x  80800)  =    -  o'44 
95'4  x  56 

In  general  Nv  varies  from  -  0*4  to  -  i'o 

A  mathematical  expression  can  also  be  deduced  for  Nv  but 
whereas  in  the  case  of  Lv  the  effect  of  the  body  and  fins  is  very 
small  in  comparison  with  that  of  the  wings,  and  can  therefore  be 
neglected  for  most  cases,  such  is  not  the  case  with  Nv,  the  fin 
surfaces  having  a  very  important  effect  upon  the  value  of  this 
derivative.  The  yawing  moment  due  to  side-slip  depends 
primarily  upon  the  body  and  fins,  and  its  value  is  determined 
by  the  proportion  of  body  and  fin  surface  before  and  behind 
the  C.G.  The  mathematical  expression  will  therefore  contain  a 
term  very  similar  to  that  due  to  the  wing  surfaces  in  Lv,  together 
with  terms  in  which  the  position  of  the  fin  surfaces  relative  to 
the  C.G.  is  taken  into  account. 


STABILITY  325 

Yp    Variation  of  Lateral  Force  with  Rolling.  —  The 

lateral  force  produced  by  rolling  is  principally  due  to  the 
dihedral  angle  between  the  main  planes,  and  is  unimportant  in 
the  stability  equations. 

Lp  The  variation  of  Rolling  Moment  due  to  Rolling. 

—  The  value  of  this  derivative  depends  almost  entirely  upon  the 
wings,  and  can  be  calculated  with  sufficient  accuracy  from  the 
results  of  the  usual  aerofoil  tests  in  the  manner  shown  below. 
This  is  the  method  most  frequently  adopted.  A  roll  increases 
the  angle  of  incidence  of  the  falling  wing  and  decreases  that  of 
the  rising  wing.  Let  /  be  the  angular  velocity  of  wings  about 
the  axis  of  x  :  then  the  increase  in  the  angle  of  incidence  due  to 
this  velocity  (/) 


and  increased  lift  on  falling  element 

t       .  d   Kv  O     j  j  /TT-7 

=  b  i  —  —  ?  •   "  b  .  d  y  .  U2 
di       g 


o 

Moment  of  element 

-  -P.y.>.dy.tg.'v.d-%.y 

Total  Moment          =  \  m  .  /  .  Lp 

=     -pP.'M.bAff      dy 

g  dt  J  J 

o 

That  is,  for  wings  of  rectangular  plan  form 

Ley          O            ,TT         d   K.y          ,  ,  q 

D     =        —      ^    — ! .      U     .    *    .    U    ,    U 

*  gm  di 

The  value  of  Lp  will  be  considerably  affected  by  4  End 
Effect,'  and  in  order  to  obtain  the  most  accurate  results  it 
is  necessary  to  take  this  loss  into  account.  The  greater  the 
aspect  ratio  of  the  wings  the  less  important  does  this  correction 
become. 

For  small  machines  Lp  'varies  from  —  200  to  —  400,  while 
for  machines  of  20,000  Ibs.  in  weight  its  value  approaches  —  2000. 

An  example  of  this  is  shown  by  applying  formula  to  the 
case  of  the  Bleriot  machine.  Then 


"  3 x  ~?6  x  95'4  x  '°45  x  5rs  x  12 x     x 
=  - 195 


326  AEROPLANE    DESIGN  „  ' 

The  experimental  value  of  the  derivative  was  —  167  and  the 
discrepancy  is  largely  due  to  the  fact  that  no  correction  was 
made  for  *  end  effect.'  The  aspect  ratio  of  the  Bleriot  machine 
is  low,  and  consequently  there  would  be  a  considerable  reduction 
in  the  average  dY^^di  over  the  wing  surface.  Assuming  the 
value  of  the  lift  coefficient  to  vary  in  accordance  with  a  para- 
bolic law  over  the  outer  section  for  a  distance  equal  to  the  wing 
chord,  the  average  value  of  Ky  for  the  Bleriot  wing  surface  will 
be  approximately  0*83  x  max.  Ky .  The  value  of  the  deriva- 
tive Lp  would  now  become  —  195  x  0*83  =  —  162,  which  is  in 
very  close  agreement  with  the  experimental  value.  A  much 
more  accurate  method  of  taking  into  account  '  end  effect '  is  to 
solve  the  integral 

/*-&#? 

graphically,  and  to  substitute  the  value  thus  obtained  in  the 
general  formula.  Such  a  method  would  of  course  necessitate  an 
accurate  knowledge  of  the  variation  of  the  lift  coefficient  over 
the  whole  span. 

The  experimental  method  of  determining  Lp  is  to  mount 
the  model  of  the  machine  upon  the  balance  in  such  a  manner 
that  it  is  free  to  rotate  about  a  horizontal  axis.  The  model  is 
oscillated  by  means  of  a  spring  against  the  damping  present  due 
to  the  wind  forces  and  frictional  losses  in  the  apparatus  for  a 
period  of  from  20  to  40  seconds.  The  oscillations  are  photo- 
graphically recorded  for  several  wind  speeds  and  provide  a 
means  of  estimating  the  damping  coefficient  due  to  the  relative 
wind,  and  this  is  the  derivative  required. 

Np  The  variation  of  Yawing  Moment  due  to 
Rolling. — It  has  been  seen  that  the  value  of  Lp  depends  upon 
the  slope  of  the  lift  curve  for  the  wing  section  employed.  It 
follows  that  the  yawing  moment  due  to  rolling  must  depend 
chiefly  upon  the  slope  of  the  drag  curve.  The  value  of  Np  may 
tneretore  be  written 

7   T7- 

bd* 


3  g m          di 

The   effect  of  the  body   and    fins   will  be  very  small  in    most 
machines. 

The  ratio  of  the  slopes  of  the  Lift  and  Drag  Curves  at 
angles  slightly  greater  than  those  giving  maximum  Lift/Drag 
is  usually  in  the  neighbourhood  of  10,  hence  the  value  of 
Np  will  be  about  one-tenth  that  of  Lp  at  these  angles.  Also 
since  the  slope  of  the  drag  curve  may  become  zero,  the  value  of 


STABILITY 


327 


Np  when  the  machine  is  flying  at  the  angle  of  minimum  drag  of 
the  wings  must  be  zero.  Np  is  found  to  vary  between  o  and  40 
for  small  machines,  and  increases  up  to  300  in  large  machines. 

The  experimental  determination  of  Np  is  a  somewhat 
difficult  matter,  the  method  adopted  being  similar  to  that 
used  for  the  determination  of  Lr  which  will  be  described  later. 
For  the  Bleriot  machine  the  experimental  value  was  24. 

Using  the  formula  we  have 


di 


•005  x  57'3 


whence 


•00237 
3  56 


=  -  x      -^    x  95-4  x  -005  x  57-3  x  f-  x  (-»-     x  20* 


12 


=    22 


Yr   Yariation  of  Lateral  Force  due  to  Yawing.— 

This  derivative  has  practically  no  effect  upon  the  stability  of  an 
aeroplane,  and  its  value  can  therefore  be  neglected. 


r 


FIG.  239. 

Lr   Yariation   of  Rolling  Moment  due  to  Yawing. 

— The  value  of  this  derivative  is  largely  dependent  upon  the 
wing  surfaces  of  a  machine.  Its  experimental  determination  is 
not  easy,  as  it  is  necessary  to  produce  a  forced  oscillation  of 
known  magnitude  about  one  axis  of  rotation,  and  to  measure 
the  corresponding  oscillation  about  a  second  axis  of  rotation 
perpendicular  to  the  first.  The  model  is  arranged  to  be  free  to 
rotate  about  the  axes  of  roll  and  yaw,  the  rolling  motion  being 
controlled  by  a  stiff  spring  so  that  the  model  can  oscillate  in 
sympathy  with  an  impressed  force  of  suitable  period.  An 
oscillation  is  then  set  up  about  the  axis  of  yaw,  and  the  period 
of  oscillation  about  the  axis  of  roll  is  adjusted  until  resonance  is 
obtained  ;  the  required  data  can  then  be  deduced  from  a  know- 
ledge of  the  amplitude  of  the  oscillations.  The  experimental 
value  for  Lr  for  the  Bleriot  model  is  found  to  be  54. 


328  AEROPLANE    DESIGN 

MATHEMATICAL  DERIVATION  OF  Lr  —  In  yawing,  the  outer 
wing  of  the  machine  is  moving  faster  than  the  normal  speed  of 
the  machine,  while  the  inner  wing  is  moving  slower.  This  will 
cause  an  increased  lift  on  the  outer  wing  and  a  diminished  lift 
on  the  inner  wing.  If  r  be  the  angular  velocity  of  yaw,  then 
the  increased  speed  of  any  element  distant  y  from  the  axis  of 
z  =  d'U  =  ry  (see  Fig.  239),  and  the  increased  lift  on  this 
element 


=  Ky  t  /  (U' 

0>       V. 


-  U2]  b  .  dy 

,i 


=  Ky  £  2  .  'U  ry  b  .  dy 

V 

and  Moment  of  Element 

-  Ky  £  2.  'Ur/  £.</>' 

o 

whence     J  m  r  Lr  =  Ky  ^-£  'U  r   A  .f*  ,  dy 

o  +J 

O 

That  is,  for  wings  of  rectangular  plan  form 

Lr  =  4_£_  Ky'UJ*/8 
$gm 

For  the  Bleriot  machine  the  calculated  value  of  Lr 

=  1  x    00237  x  0-^8  x  0=5-4  x  —  x  (---]  x  204 

3  56  12          VX2/ 

=  58  as  compared  with  the  experimental  value  54. 
Lr  varies  from  50  in  small  machines  to  600  in  large  machines. 

NP  Variation  of  Yawing  Moment  due  to  Yawing.  — 

This  derivative  depends  upon  wings,  body,  and  fins,  and  its 
value  must  therefore  be  determined  experimentally.  The 
method  adopted  is  similar  to  that  used  in  the  determination 
of  Lp.  Its  value  may  be  expected  to  vary  between  —  20  and 
—  100.  For  the  Bleriot  machine  its  value  was  found  to  be  —  31. 

Application  of  Derivatives  to  Stability  Equations.  — 
From  this  enumeration  and  consideration  of  the  derivatives  it  is 
now  necessary  to  turn  to  the  question  of  the  method  of  their 
application  to  the  stability  equations. 

A.  LONGITUDINAL  STABILITY  (Period  of  Oscillation).  — 
Bairstow  has  shown,  from  an  examination  of  the  relative 
numerical  values  of  the  coefficients  in  the  biquadratic  equation, 


STABILITY  329 

that  it  can  be  factorised  to  a  first  approximation  and  expressed 
in  the  form 


This  approximation  is  sufficiently  accurate  if 
-  and  A—    are  less  than  — 

C  C2  20 

R  C* 
and  A  D  is  less  than 

20 

These  conditions  are  generally  satisfied  by  modern  machines, 
but  should  be  checked  before  proceeding  further  with  an  analysis 
of  stability. 

In  Formula  96  the  first  factor  represents  a  short  oscillation 
which  in  most  aeroplanes  rapidly  dies  out  and  is  not  of  much 
importance.  The  second  factor  represents  a  relatively  long 
oscillation,  involving  an  undulating  path  with  changes  in  pitch, 
forward  speed,  and  attitude.  It  is  termed  by  Lanchester  the 
"  phugoid  oscillation.  '  These  long  oscillations  should  diminish 
in  amplitude  with  time,  in  which  case  the  motion  is  stable  and 
the  aeroplane  will  return  to  its  original  flight  attitude  if  tempo- 
rarily deviated  therefrom  by  accidental  causes.  The  motion  is 
unstable  if  the  amplitude  increases  with  time. 

Eliminating  the  various  resistance  derivatives  of  negligible 
value,  the  formula  for  the  coefficients  in  longitudinal  stability 
(Formula  94)  can  be  written. 

A  =  kj 

B  =    -  (Mq  +  Xu£b2  +  Zw/£b2) 

C  -  Zw  Mq  -  Mw  U  +  Xu  Mq  +  k£  (XUZW  -  XWZU) 

D  =     -  Xu  Mw  U  +  Zu  Mq  Xw  -  Xu  Zw  Mq 

E  =    -  £-MwZu  ............   Formula  94  (a) 


By  substitution  of  the  values  of  the  various  derivatives  in 
the  above  formula,  the  periodic  time  of  each  oscillation  is  easily 
determined.  A  very  short  oscillation  indicates  great  statical 
stability,  and  the  machine  will  very  rapidly  resume  its  normal 
flying  attitude.  Such  a  machine  would  be  very  uncomfortable 
for  flying  purposes  on  account  of  the  violent  changes  in  motion. 
It  is  preferable  that  an  aeroplane  should  have  a  heavily  damped 
oscillation  of  long  period,  such  that  the  resumption  of  the 
normal  flying  attitude  takes  place  very  gradually.  The  aim  in 
design  should  therefore  be  to  ensure  that  the  righting  moments 
on  the  machine  are  just  sufficient  to  give  static  stability,  and  to 


330  AEROPLANE    DESIGN 

depend  upon  large  damping  surfaces  for  dynamic  stability.  It 
is  probable  that  longitudinal  stability  may  be  secured  at  all 
speeds  by  the  use  of  a  sufficiently  large  tail  plane. 

Longitudinal  Stability  of  the  Bleriot  Machine. — Collect- 
ing together  the  various  quantities  and  the  values  of  the 
derivatives  affecting  the  longitudinal  motion  of  this  machine, 
we  have 

m    =  56  Xw   =        0-152 

£b     =5  feet  Zw    =    -  2-43 

Xu    =      -    0-935  MW    -  2-21 

Zu    =        -    0-672  Mq    =      --      175 

The  values  of  the  coefficients  are  therefore 

A  =  S'2  =  25 

B  =  -  (-  175  +  "  °'°935  x  25  +  -  2-43  x  25)  =  236 
C  =  (-  2-43  x  -  175)  -  (2-21  x  -  95-4)  +  (-  0-0935  x  "  175) 
+  25  (-  0-0935  x  -  2'43  -  o-I52  x  -  -672)  =  636 

D  =  (0-0935  X  2'2I  X  -  95-4)  +  (-  0*672  X   -  175  X  0*152) 

-  (-  °'°935  x  -  2-43  x  -  175)  =  77 

E  =   —  32-2  X  2'2I  X   -  0-672   =  48 

Substituting  these  values  in  Routes  Discriminant 

236  x  636  x  77  -  25  x  yy2  -  236'2  x  48  =  8-7  x  io6 

Since  all  the  coefficients  and  Routh's  Discriminant 
are  positive,  the  aeroplane  is  longitudinally  stable. 

The  periodic  time  of  the  short  oscillation  is  determined  from 
the  first  factor  of  Formula  96. 

Substituting  the  values  obtained  above 

X*  +  ^6  x  +  636  =  Q 

25  25 

that  is  X2  +  9*44  A  +  25-4  =  o 

whence         X  =  —  4-72  ±  i"j6i 
The  imaginary  roots  indicate  an  oscillation  of  periodic  time 

— --    =3*6  seconds  approximately 
and  the  time  to  damp  50% 

-  seconds  =  o-ic;  seconds. 
4-72 


STABILITY  331 

The  periodic  time  of  the  long  oscillation  is  determined  from 
the  second  factor  of  Formula  96. 

Substituting  the  values  obtained  above 

/  76    __  236  x  48    x 
'  ~J          636 


or  X2  +  0*092  X  +  0*0754  =  o 

whence      X  =   —  0*046  ±  0*271  / 
The  period  of  the  longitudinal  oscillation  is  therefore 

=  23  seconds 


0*2  /I 

and  the  disturbance  is  reduced  to  half  its  value  in 

—,  seconds,  that  is  in  about  1 s  seconds. 

0-046 

The  mathematical  treatment  given  in  the  foregoing  para- 
graphs has  been  extended  by  the  N.P.L.  to  show  the  motion  of 
this  aeroplane  during  recovery  from  gusts  and  movements  of 
the  controls.  Fig.  240  shows  the  disturbed  longitudinal  motion 
due  to  a  single  horizontal  gust.  As  a  result,  the  velocity  of  the 
aeroplane  relative  to  the  air  is  increased  by  a  small  amount,  u0. 
This  increase  rapidly  dies  away,  and  after  5  seconds  becomes 
zero  ;  the  velocity  goes  on  decreasing  for  a  further  5  seconds, 
reaching  its  minimum  value  at  the  end  of  10  seconds.  This 
velocity  then  increases  again  for  a  period  of  about  10  seconds 
before  commencing  to  diminish  again.  The  changes  appear  to 
follow  a  periodic  curve  of  rapidly  decreasing  amplitude,  such 
as  would  be  obtained,  for  example,  from  the  projection  of  a 
logarithmic  spiral,  and  after  about  50  seconds  are  completely 
damped  out.  The  change  of  velocity  of  the  machine  normal  to 
the  air  is  w,  and,  as  will  be  seen  from  Fig.  240,  this  commences 
from  zero,  reaches  a  maximum  value  of  about  *2  «,  and  then 
dies  away  rapidly  in  the  same  manner  as  u.  Curves  for  q  the 
angular  velocity  of  the  machine  (shown  dotted),  and  for  0  the 
angle  of  pitch,  are  also  shown  to  a  greatly  enlarged  scale.  It 
will  be  seen  that  the  pitch  angle  increases  for  about  5  seconds 
and  then  diminishes  again,  being  finally  brought  to  zero  through 
a  series  of  periodic  changes  of  decreasing  amplitude  and  of 
22  seconds  period. 

The  corresponding  case  in  practice  arises  when  the  machine 
is  struck  by  a  horizontal  gust.  The  lift  on  the  wings  will  be 
momentarily  increased  and  the  machine  will  begin  to  climb  ; 
that  is,  there  will  be  a  component  of  velocity  w  normal  to  the 
direction  of  flight.  The  nose  of  the  machine  will  be  inclined 


332 


AEROPLANE    DESIGN 


upwards  ;  that  is,  an  angular  velocity  q  is  set  up,  and  the 
angle  of  incidence  of  the  wings  is  increased  by  an  amount  9. 
The  result  of  the  gust,  however,  will  be  to  reduce  the  velocity  of 
the  machine,  and  after  it  has  passed  the  lift  on  the  wings  will  be 
insufficient  to  support  the  machine.  It  therefore  commences  to 


20    24    28    32    36    40    44    48    52    56   So 


TJME    IN   SECONDS 


FIG.  240.  —  Disturbed  Longitudinal  Motion  of  an  Aeroplane 
(Single  horizontal  gust). 


TTME  IN  SECONDS. 


FIG.  241. 


-Disturbed  Longitudinal  Motion  of  an  Aeroplane 
(Single  downward  gust). 


fall,  and  in  so  doing  picks  up  speed  again.  On  account  of  its 
momentum,  however,  its  velocity  increases  to  a  greater  extent 
than  is  required  for  equilibrium,  and  the  machine  will  then 
flatten  out  and  commence  to  climb  again,  the  cycle  of  opera- 
tions being  repeated  until  the  oscillation  dies  away  through  the 
damping  out,  owing  to  the  action  of  the  control  surfaces.  The 


STABILITY  333 

motion  is  therefore  seen  to  be  stable,  and  the  machine  settles 
down  to  its  original  speed  relative  to  the  wind  in  less  than  a 
minute. 

A  second  curve,  Fig.  241,  was  prepared  to  show  the  effect  of 
a  downward  gust  upon  the  machine.  By  combining  the  results 
of  these  two  diagrams,  it  is  possible  to  find  the  effect  of  a 
steady  gust  of  wind  striking  the  machine  in  any  direction  in 
the  plane  of  symmetry. 

Recent  investigations  upon  the  stability  of  full-size  machines 
by  the  use  of  cinematography,  show  that  the  mathematical 
theory  is  borne  out  with  considerable  accuracy  in  practice. 

B.  LATERAL  STABILITY. — The  factorisation  of  the  biquad- 
ratic equation  for  lateral  stability  as  deduced  by  Bairstow  is 

Ef  \       /  /~D'  \  2  A  '  f"1'  \      P"""  / C*1  T?'\  "D'   T\'  "H 

1    I  X    -4-   \       '  t    I    A2   4-   I  1  X    4-  - 

*~  D7/  \  A'  B'        /  L          VB7       D/          (B')2-  A'C'J 

Formula  97 
which  approximation  is  sufficiently  accurate  if 

T?'  T7'  T 

— :  and  — ,  are  less  than  — 
B  D  20 

and  B'  D'  -  (C')2  is  less  than  (C ' 

20 

The  value  of  the  coefficients  for  lateral  stability  in  horizontal 
flight  given  in  Formulae  95  be  can  reduced  to  the  simpler 
expressions 

A'  -  kj  k<? 

B'  =   -  Yv  (Lp  Nr  -  Np  Lr)  +  Lp  k<?  +  Nr  k£ 

C  =  Yv  (Lp  k«~  +  Nr  k^}  -  U0  Nv  kj  +  Lp  Nr  -  Np  Lr 

D'  =  U0  (U  Np  -  Lp  Nv)  -  Yv  (Lp  Nr  -  Np  L,) 

+  g  (U  k<?  -  Nv  kjf) 
E'  =   -  g  (Ly  Nr  -  Nv  Lr)  Formulss  95  (a) 

By  far  the  most  important  item  in  the  biquadratic  (Formula  97) 

E' 
is  the  first  factor,  namely,  (\  +   — )  =  0.    If  the  machine  be  stable 

this  factor  represents  a  subsidence  the  amplitude  of  which  will 

0^69 
be  reduced  50%  in     E'    seconds.     If  E'  and  D'  be  of  opposite 

D' 

sign,  instability  will  arise,  and  for  present-day  machines  the 
criterion  that  Er  is  positive  is  the  most  important  consideration 
for  lateral  stability,  and  is  also  the  most  difficult  condition  to 
obtain.  In  order  that  Er  may  be  positive,  it  will  be  seen  from 
the  signs  of  the  various  derivatives  that  numerically  LV/NV 


334  AEROPLANE    DESIGN 

should  be  greater  than  Lr/Nr.  The  physical  explanation  of  this 
result  is  comparatively  easy  to  understand.  Lv  and  Lr  are  the 
rolling  moments  due  to  side-slip  and  yawing  respectively,  the 
former,  as  will  be  seen  from  the  mathematical  expression,  being 
dependent  on  the  dihedral  angle,  and  the  latter  on  the  increased 
lift  of  the  outer  wing  when  turning.  A  side-slip  inwards  tends 
to  reduce  the  banking  whilst  the  turn  tends  to  increase  it,  and 
instability  occurs  when  the  latter  becomes  the  greater.  Lv  can 
be  increased  by  making  the  dihedral  angle  greater,  but  Lr  is 
difficult  to  control. 

The  derivatives  Nv  and  Nr  depend  upon  the  relative  rates  of 
side-slipping  and  turning  of  the  body  surface  and  rudder  area. 
Nv  can  be  reduced  by  using  a  small  rudder,  but  this  has  obviously 
the  disadvantage  of  reducing  the  control,  and  would  tend  to 
produce  a  form  of  instability  known  as  '  spin,'  in  which  the 
machine  will  rotate  about  a  vertical  axis  through  its  centre  of 
gravity.  Too  large  a  fin  area  will  produce  instability  of  a 
different  and  more  dangerous  kind.  This  is  shown  mathe- 
matically by  Nv  assuming  a  large  negative  value,  and  this  will 
make  E'  negative.  The  physical  explanation  is  as  follows. 

Suppose  the  machine  to  be  accidentally  banked.  It  com- 
mences to  move  in  a  circular  path,  the  axis  of  the  body  no 
longer  lying  along  the  direction  of  flight.  This  introduces  a 
large  lateral  force  if  the  rear  fin  surface  is  great,  and  the  body 
will  be  swung  round  and  tend  to  coincide  with  the  direction  of 
flight.  This  will  involve  a  still  greater  velocity  of  the  outer 
wing,  and  the  increased  lift  obtained  thereby  will  further  increase 
the  banking.  The  large  fin  area  continuously  operating  there- 
fore continually  reduces  the  radius  of  the  turn,  and  at  the  same 
time  the  lift  on  the  wings  will  be  constantly  diminishing,  so  that 
the  machine  will  be  gradually  falling.  A  continuation  of  these 
conditions  leads  directly  into  the  dangerous  motion  known  as 
the  '  spiral  nose  dive,'  and  a  machine  liable  to  such  motion  is 
said  to  be  spirally  unstable. 

In  order  to  avoid  spiral  instability  it  is  necessary  that  the 
arrangement  of  fin  surfaces  is  such  that  when  the  machine  side- 
slips to  one  side  it  will  bank  suitably  to  make  a  turn  in  the 
opposite  direction.  This  will  cause  it  to  resume  its  normal 
attitude.  ^.Such  an  effect  may  be  produced  by  having  the  major 
portion  of  the  fin  surface,  including  the  side  area  of  the  body, 
above  the  C.G.  of  the  machine.  J 

From  the  preceding  paragraph  it  will  be  seen  that  the  fin 
surface  of  a  machine  must  be  within  certain  definite  limits  if 
instability  is  to  be  avoided,  and  it  is  in  this  connection  that  the 
mathematical  analysis  will  be  of  increasing  value. 


STABILITY  335 

The  readiest  means  of  producing  stability  occurs  in  the 
changes  which  can  be  made  in  the  value  of  Nr  and  this  can  be 
increased  without  affecting  Nv  by  putting  equal  areas  before  and 
behind  the  C.G.,  a  part  played  to  some  extent  by  the  fuselage  of 
most  machines. 

(B')2  —  A'  C' 
The  second  factor  X  +  v  —  '---,-  ^  —  -  =  o  represents  for  stability 

A    -D 

a    subsidence    of    which    the    amplitude    is    reduced    50%    in 

•69  A'B'  (B')2  -  A'C 

/"DMT  -  A*  /•-'  seconds,  and   for  instability  to  occur  /rrw  — 

(Jj  J"  —  A  U  A  r> 

must  be  negative.  None  of  the  quantities  involved  in  A',  B',  C' 
is  liable  to  vary  in  such  a  way  as  to  render  this  expression 
negative  for  ordinary  conditions  of  flight,  and  the  equation 
represents  a  rolling  of  the  aeroplane,  which  is  heavily  damped 
by  the  wing  surfaces.  In  the  case  of  a  stalled  machine,  how- 
ever, this  motion  would  lead  to  trouble,  since  the  damping  effect 
produced  by  the  increased  lift  on  the  downward-moving  wing 
will  no  longer  operate.  Under  such  circumstances  a  movement 
of  the  wing  flaps  will  no  longer  produce  any  righting  moment. 
The  third  factor  may  be  written  approximately 


and  the  motion  represents  a  damped  oscillation  of  period 


A    A    B/ 

2   7T     Y 

and  damping 


3C' 
C 
2  B' 

The  third  oscillation  consists  of  a  combined  yawing  and 
rolling  motion,  and  for  stability  the  amount  of  fin  surface  above 
the  C.G.  should  not  be  excessive,  while  there  should  be  sufficient 
fin  surface  on  the  tail.  It  will  be  seen  that  these  requirements 
clash  with  those  for  spiral  stability,  but  it  is  possible  by  a  careful 
adjustment  of  the  surfaces  to  satisfy  both  conditions. 

Lateral  Stability  of  the  Bleriot  Model.— Applying  the 
equations  of  motion  to  the  case  of  the  Bleriot  Model,  its  lateral 
stability  may  be  investigated.  v  The  derivatives  concerned  are — 

Yv  =   —  0*108  Np  =   —  0*44 

Lv  =        07  Lp  =        167 

Np  =24  Lr  =         54 

Nr  =  -  31 
The  radii  of  gyration  of  a  machine  can  be  calculated  from 


336  AEROPLANE    DESIGN 

the  scale  drawings  in  the  manner  indicated  for  a  streamline  strut 
in  Chapter  IV.,  and  in  the  case  of  the  Bleriot  were  found  to  be 

/£A  (radius  of  gyration  about  axis  of  roll)  =  5' 
kc  (radius  of  gyration  about  axis  of  yaw)  =  6' 

Substituting  these  values  in  the  stability  equation,  the  values 
of  the  coefficients  are  found  to  be 

A'  is  900;  B'  is  6780;  C  is  5580;  D'  is  6640;  E'  is  -  68 
whence  Routrfs  discriminant 

=  B'CD'  -  A'D'2  -  B'2E' 

=    2  I  '5    X    1C10 

The  coefficient  of  E'  being  negative,  the  machine  is 
laterally  unstable. 

Considering  the  first  factor  of  the  equation,  we  have 
/  =  -  E'/D'  =  -  (-  68/6640)  =  -0102 

As  /    is   positive,   the    motion    is    not   oscillatory,  and   the 
amplitude  will  increase  and  double  itself  in  time, 

=  o'6q/'oio2  =  68  seconds. 
Considering  the  second  factor,  we  have 
/=  -  671 

This    represents    a    steadily    damped    motion,    which     will    be 
reduced  to  half  its  value  in 

0-69/6-7  1  =  o'i  seconds. 
The  third  factor  of  the  equation  becomes 


and  the  roots  are 

p  =  -  0*416  ±  0^963  i 

The  period  of  oscillation  will  be 

2  ^     =6-5  seconds 
0-963 

and  the  amplitude  will  be  reduced  to  one-half  in 
0-69/0-416  =  1-65  seconds. 

We  thus  see  that  the  machine  under  consideration  is  spirally 
unstable,  which  is  shown  by  the  fact  that  the  coefficient  E'  is 
negative,  that  is,  LV/NV  is  less  numerically  than  Lr/Nr  Refer- 
ence to  the  mathematical  expressions  for  these  derivatives  will 


STABILITY 


337 


show   that   in   order   to    eliminate   the   spiral    instability   it   is 
necessary  to  have 

Lv  large,  that  is  a  good  dihedral. 
Nv  small,  that  is  a  smaller  rudder. 

The  other  two  derivatives  are  difficult  to  control,  but  Nr  may 
be  increased  by  adding  equal  fin  areas  in  front  of  and  behind 
the  centre  of  gravity  of  the  machine,  and  this  will  not  affect  the 
value  of  Nv 

A  graphical  representation  of  this  lateral  or  asymmetric 
motion,  prepared  upon  the  same  lines  as  for  the  longitudinal 
motion,  is  shown  in  Figs.  242,  243.  Since  this  lateral  motion  is 
unstable,  they  differ  essentially  from  those  shown  for  the  longitu- 


o    s 

to 

§ 

H      25 


046  II  16  30  34          29  3?  36  4O          4<»  48 

TIME  IN  SECONDS 
FIG.  242. — Disturbed  Lateral  Motion  of  an  Aeroplane. 

dinal  motion.  Fig.  242  shows  the  effect  of  suddenly  banking 
the  machine  through  an  angle  <f>.  It  will  be  seen  that  after  a 
slight  subsidence  the  angle  of  bank  .increases  continuously,  and 
after  40  seconds  exceeds  its  original  value  by  more  than  60  per 
cent  At  the  same  time  the  velocity  of  side-slip  (v)  also 
increases  rapidly  in  a  negative  direction.  The  machine  there- 
fore turns  to  the  right,  the  angle  of  bank  together  with  the 
velocity  of  side-slip  increasing,  and  the  machine  falls  with 
increasing  speed. 

Fig.  243  shows  the  effect  of  a  side  wind  v"  striking  the 
machine  on  the  left-hand  side.  The  sideways  motion  is  very 
rapidly  damped  down,  but  after  about  seven  seconds  commences 


338 


AEROPLANE   DESIGN 


to  increase  again  very  gradually,  and  unless  the  controls  are 
altered  this  velocity  of  side-slip  will  continue  to  increase.  The 
velocity  of  roll  (p)  grows  very  rapidly  at  first,  but  after  two  or 
three  oscillations  is  reduced  almost  to  zero  before  commencing 
a  gradual  increase,  which  will  necessitate  an  alteration  of  the 
controls  if  it  is  to  be  checked. 

Longitudinal  Stability  of  a  Biplane. — A  more  recent 
investigation  of  the  longitudinal  stability  of  a  machine  was 
carried  out  at  the  Massachusetts  Institute  of  Technology  by 
Hunsaker,  and  is  described  in  the  U.S.A.  Advisory  Committee 
Report  for  1914.  The  machine  was  a  Curtiss  Biplane,  and  the 


Time   in    Seconds 

FIG.  243. — Disturbed  Lateral  Motion  of  an  Aeroplane. 


model   which    is    shown    in    Fig.   244  (a  b  c]  was    made  one- 
twenty-fourth  full  size,  and  geometrically  similar  to  its  prototype. 
The  leading  dimensions  of  this  machine  are  as  follows  : — 


Weight,  iSoolbs. 
Total  wing  area,  384  sq.  ft. 
Area  of  tail,  23  sq  ft. 
Area  of  elevator,  ipsq.  ft. 
Area  of  rudder,  7*8  sq.  ft. 


Span,  36  ft. 
Chord,  5  ft.  3  ins. 
Gap,  5  ft.   3  ins. 
Length  of  body,  26  ft. 


The  model  was  mounted  on  the  balance,  with  its  wings  in 
the  vertical  plane,  and  the  Lift,  Drag,  and  Pitching  Moment 
were  measured  for  various  angles  of  wing  chord  to  the  wind. 

These   results   are   exhibited    graphically  in   Fig.    245,  the 


STABILITY 


339 


forces  being  given  direct  in  Ibs.,  and  the  moments  in  Ibs.  inches. 
The  wind  velocity  was  30  m.p.h. 

The  axes  of  reference  are  assumed  fixed  in  the  aeroplane 


EL 


FIG.  244. — Model  Curtis  Biplane. 


and  moving  with  it  in  space,  with  the  origin  at  the  centre  of 
gravity.  For  steady  horizontal  flight  at  a  given  attitude  the 
axis  of  '  z'  is  vertical,  and  the  axis  of  '  x*  is  horizontal.  Angles 
of  pitch  departing  from  the  normal  flying  attitude  will  be 


340 


AEROPLANE    DESIGN 


denoted  according  to  the  table  by  9.     For  equilibrium  6  is,  of 
course,  zero. 

At  high  speed  (79  m.p.h.)  the  axis  of  ' x'  was  horizontal, 


FORCES 


&,  MOMENTS 


ON  MODEL 


Wind  Spe«  d    50  m.p  h 


4-°  8* 

Angle     of     Incidence 


FIG.  245. — Forces  and  Moments  on  Model  of  Curtis  Biplane. 


and  made  an  angle  of  i°  with  the  wing  chord  ;  while  at  low 
speed  (45  m.p.h.),  with  the  axis  of  ' x*  still  horizontal,  this  axis 
made  an  angle  of  12°  with  the  chord.  The  axes  are  fixed  by  the 
equilibrium  conditions  for  flight,  and  differ  for  each  normal 
flying  attitude 


STABILITY  341 

It  was  found  convenient  for  wind-tunnel  purposes  to 
measure  the  lift  and  drag  about  axes  always  vertical  and 
horizontal  in  space.  To  transform  these  axes  to  those  re- 


Angle   of    Rt-cVi  (9) 
+  3"  *7* 


\ 


Angle     of  Incidence  (i.) 

Caoel          V/-79n>p.-h. 
I  •  f  i° 


FIG.  246. — Forces  and  Moments  on  Model  of  Cuitis  Biplane. 


quired    for    stability   investigation    the   following   relationships 
are  used  : 

m  Z   =  L  cos  6  +  D  sin  0 

m  X  =  D  cos  S  -  L  sin  0 

By   the   use   of  these   formulae   and   reference  to   Fig.  245, 
Tables  XLVIL  and  XLVIII.  were  calculated. 


342 


AEROPLANE    DESIGN 

TABLE  XLVIL—  (CASE  I.) 
Speed,  79  m.p.h.     Angle  of  attack  (i)  i' 


i 

6» 

L 

D 

Z 

X 

-  4 

-  5 

-  0-08 

'"5 

-  6-4 

77 

0 

—  i 

'35 

'IO2 

24-9 

7-76 

4 

3 

765 

•118 

54'9 

5'6 

8 

7 

*'I3 

•165 

81-0 

1-9 

12 

ii 

J'39 

•270 

lOO'O 

'7 

16 

i5 

1-48 

•428 

109-0 

-  2-05 

TABLE  XLVIII.— (CASE  II.) 
Speed,  45  m.p.h.     Angle  of  attack  (/)  12' 


i 

61 

L 

D 

Z 

X 

8 

-  4 

•13 

•165 

26-1 

5-68 

10 

-    2 

•28 

*2I 

29-6 

5-33 

12 

O 

'39 

•27 

32>4 

6*29 

14 

2 

•45 

•348 

34'° 

6*92 

16 

4 

•48 

•428 

35'2 

7-56 

These    results  £are    shown   graphed   in    Figs.    246  and  247 
From  these  curves  the  values  of 

JX    dZ     dM 

7-6  -TV  70 

are  read  off,  and  the  values  are  then  inserted  in  the  formulae  for 
derivatives  XW^ZW  and  Mw 

Case  L— 

=,      _  57.3     dX 

~\r  Je 

_  57'3  x    -  "65 

-    115*5    X    2 
=    '162 

Note  that  U  is  negative,  as  explained  previously. 


7      _  57'3 
"IT 

57'3 


d~B 


-  "5'5  x  4 

-  3'95 


STABILITY  343 


_  57-3     dM 
U       dQ 


57'3 


x 


-  ii5'5  x  4 

=  174 

2  x  Drag 

~  -  TT  - 

m  U 

_  2  x  -104  x  242  x  (V/3o)2 

32  x  -  "5*5 

:          -128 

2   x     • 


2    X    32*2 

-  "5*5 

=  -  -557 
By  experiment  the  value  of  Mq  was  found  to  be  —  1  50. 

The  radius  of  gyration  of  the  machine  about  the  axis  of  pitch 
was  experimentally  found  to  be  5*8  feet,  which  gives  us  at  once 
the  value  of  £b. 

By  substituting  in  the  various  values  of  the  derivatives  the 
values  of  the  coefficients  are  found  to  be 

A  =  '5'82  -  34 

B  =    -  (-  15°  -  "128  x  34  -  3-95  x  34) 
-  289 

c  =  3'95  x  15°  +  i'74  x   115-5  +  34('i2   x  3-95  +  '162  x  -557) 
=  834 

D=  -128  x  1-74  x  113*5  +  '557  x  150  x  -162  +  '128  x  3-95  x  150 

=  IJ5 

E  =  32-2  x  174  x  -557 
3i 

Substituting  these  values  in  Routh's  Discriminant  we  get  that 
the  discriminant 

=  289  x  834  x  115  -  34  x  ii52  -  2892  x  31 

=     18  x  io6 

Since  Routh's  Discriminant  and  all  the  coefficients  are 
positive,  the  machine  will  be  longitudinally  stable  at  the  speed 
considered,  namely  79  m.p.h. 


344  AEROPLANE    DESIGN 

The  short  oscillation 

=  X2  +  8-5  X  +  24-5  =  o 
whence  \  =  —  4-25  ±  2*54  i 

The  period  =        P  =  2  7r/2'54  =  2*5  seconds 
The  time  to  damp  out  5o°/0 

=  0-69/4-25  =  -16  seconds 
The  long  oscillation 

=  X2  +  '125  X  +  "0374  =  o 
whence  /  =   -  '063  ±  'i83/ 

The  period  of  this  long  oscillation 

=  P'  =  34'3  seconds 
and  time  to  damp  50  °/o 

=  /  =  io'8  seconds 

The  small  oscillations  are  thus  seen  to  be  unimportant  while 
the  long  oscillations  are  strongly  damped.  The  aeroplane  should 
therefore  be  very  steady  at  this  speed. 


Case    E 

\  V  »  45  £  mph 

I  L  .  «• 


Angle     of     Pil-ch  (6) 


FIG.  247. — Forces  and  Moments  on  Model  Curtis  Biplane. 

Case  II. — Speed,  45  m.p.h  (66  f.p.s.)  ;  incidence,  12°.  Pro- 
ceeding in  a  similar  manner,  the  values  of  the  derivatives  at  this 
speed  are  found  to  be 

Xu  =  -  -189  Zu  =  -972  Mw  =  2-15 


Xw  =  -  -236 


•972 
Z»-  =  736 


Mq  =   -  106 


STABILITY  345 

and  the  values  of  the  coefficients  are 

A  =     34  C  =  243  E  =  67-2 

B  =  137-5  D  =     *7'4 

whence  Routh's  Discriminant 

=  137-5  x  243  x  17-4  -  34  x  i7*42   -  i37*52  x  67-2 
=   -  7  x  io5 

which  being  negative  indicates  that  the  machine  will  be  unstable 
at  this  speed. 

The  short  oscillation 

=  X2  +  4*04  X  4-  7 '14  =  o 

whence  X  =  -  2*02  ±  1*75* 

and  the  period  =  3'59  seconds 

and  the  time  to  damp  out  5o°/o  =  0*342  seconds 

The  long  oscillation 

=  X2  -  0*085  X  -f  '276  =  o 

whence  X  =  0*043  —  "524* 

and  the  period  =12*0  seconds 

and  the  time  to  double  amplitude  =  16  seconds. 

The  machine  is  thus  seen  to  be  unstable  at  a  speed  of 
45  m.p  h.,  and  it  is  essential  that  the  pilot  should  keep  a  firm 
hold  on  his  elevator  control. 


CHAPTER   XL 
DESIGN  OF  THE  CONTROL  SURFACES. 

Controllability  and  Stability.— The  question  of  the  rela- 
tion between  the  control  and  stabilising  surfaces  was  briefly 
considered  in  the  preceding  chapter  on  stability,  and  it  was 
stated  that  the  degree  of  controllability  of  a  machine  was 
determined  generally  by  the  duties  for  which  it  was  to  be  used. 
For  fighting  purposes  it  is  necessary  that  the  machine  should 
answer  very  quickly  to  the  controls,  and  hence  its  static  stability 
must  be  small ;  whereas  in  the  case  of  a  large  commercial 
machine  with  which  long  journeys  must  be  undertaken,  the 
static  stability  can  with  great  advantage  be  considerably  in- 
creased. 

In  general  it  is  preferable  to  keep  the  static  stability  as  low 
as  possible,  and  to  obtain  dynamic  stability  by  using  large 
wings  and  stabilising  surfaces.  The  problem  of  static  stability 
can  be  considered  as  under.  In  nearly  all  the  modern  machines 
the  stabilising  surfaces  are : 

(a)  The  Tail  Plane  and  Elevator. 

(b)  The  Rudder  and  Fin. 

Of  these  the  elevator  is  also  the  control  surface  for  longitudinal 
flight  and  the  rudder  for  directional  flight,  while  ailerons  or 
wing-flaps  control  the  rolling  motion  of  a  machine. 

The  Tail  Plane  and  Elevator. — The  tail  plane  and 
elevator  in  an  aeroplane  of  normal  design  are  essentially  those 
members  which  are  intended  to  give  the  machine  that  longi- 
tudinal stability  which  the  wing  surface  alone  lacks.  It  will  be 
remembered  from  Chapter  III.  that  over  the  range  of  normal 
flying  angles  the  C.P.  of  an  aerofoil  moves  forward  as  its  angle 
to  the  wind  direction  is  increased.  The  resulting  effect  upon 
the  machine  is  illustrated  by  the  diagrams  in  Fig.  248. 

If  it  be  assumed,  as  shown  in  case  (£),  that  at  that  particular 
instant  the  line  of  lift  passes  through  the  C.G.  of  the  machine, 
then  there  will  be  no  moment  upon  the  machine,  and  conse- 
quently no  load  upon  the  tail.  If,  however,  a  upward  gust  of 
wind  strikes  the  machine,  the  angle  of  incidence  of  the  wings 
to  the  resultant  wind  direction  will  for  a  very  short  time  be 
reduced,  the  C.P.  will  move  backward  to  the  position  shown  in 
case  (a),  and  a  pitching  moment  will  be  set  up  upon  the  machine 


DESIGN    OF   THE    CONTROL   SURFACES 


347 


which  must  be  counterbalanced  by  the  tail  plane  surface  if 
equilibrium  is  to  be  restored.  Similarly  in  case  (c\  if  the  angle 
of  incidence  relative  to  the  wind  direction  has  been  temporarily 
increased,  then  a  stalling  moment  will  be  set  up  and  the  tail 
plane  will  be  called  upon  to  produce  a  righting  moment. 


Co) 


r 


FIG.  248. — Direction  of  Load  on  the  Tail  Plane. 


Moreover,  by  reference  to  the  fundamental   equation  (For- 
mula i),  it  will  be  seen  that 


Normal  force 


g 

=  W  cos  / 


or 


/  W  cos  i 

=  v  - 


v=  A 


for  case  (b) 


348  AEROPLANE    DESIGN 

from  which  it  follows  that  the  attitude  of  the  machine  for 
equilibrium  varies  with  the  speed.  The  righting  moment  to  be 
exerted  by  the  tail  plane  and  elevator  will  therefore  depend 
upon  the  speed  at  which  the  machine  is  flying.  Conversely,  an 
adjustment  of  the  tail  plane  and  elevator  will  alter  the  pitching 
moment  upon  the  machine,  and  so  lead  to  an  alteration  in  its 
attitude  and  speed. 

A  further  deduction  from  the  preceding  paragraph  is  that 
the  successful  design  of  a  tail  plane  for  a  particular  machine 
will  depend  largely  upon  its  speed  range  ;  for  it  is  easy  to  see 
that,  in  a  fast  machine  with  a  wide  speed  range,  if  the  tail  plane 
is  sufficiently  large  for  the  upper  limits  of  speed,  then  it  will  be 
inadequate  for  slow  flight  unless  'more  weight  and  head  resist- 
ance are  allotted  to  it  than  would  in  most  cases  be  advisable. 
In  the  absence  of  an  easy  method  of  making  a  variable-area  tail 
— the  real  solution  to  the  above  difficulty — some  compromise 
must  be  made  in  practice. 

In  certain  cases  it  is  sometimes  found  necessary  to  displace 
the  line  of  thrust  of  the  airscrew  so  that  it  no  longer  passes 
through  the  C.G.  of  the  machine.  The  unbalanced  moment 
resulting  will  need  to  be  corrected,  and  this  duty  also  falls  to 
the  lot  of  the  tail  plane.  It  will  thus  be  seen  that  a  large 
number  of  factors  enter  into  the  design  of  the  tail  plane  and 
elevator. 

The  duty  of  the  tail  plane  does  not  require  it  to  be  cambered, 
a  flat  plane  being  all  that  is  necessary,  though  some  stream- 
lining at  the  leading  and  trailing  edges  may  help  towards 
lessening  resistance.  A  streamlined  tail  plane  can  generally 
be  designed  that  will  offer  no  extra  head  resistance,  but  will 
afford  greater  thickness  and  greater  strength,  combined  with 
better  accommodation  for  a  strong  hinge-spar  for  the  elevator 
lift  The  tail,  moreover,  need  normally  exert  no  lifting  force  ; 
but  this  non-lifting  or  'floating'  tail  will  only  be  so  at  certain 
angles — that  is,  at  certain  speeds  of  the  machine. 

When  the  disposition  of  the  tail  plane  is  such  that  the  tail 
exerts  a  downward  force,  it  is  found  that  the  stability  of  a 
machine  is  increased,  and  this  arrangement  is  frequently  adopted 
in  modern  design.  Should,  however,  the  line  of  thrust  of  the 
airscrew  fall  below  the  horizontal  line  through  the  C.G.  of  the 
machine,  an  upward  load  on  the  tail  is  necessary.  Either 
arrangement  causes  an  increase  of  gliding  angle,  and  may, 
if  carried  to  excess,  decrease  the  useful  angular  range  of 
the  machine,  owing  to  the  proximity  in  one  direction  of  the 
critical  angle.  In  considering  the  tail  plane  as  a  stabilising 
surface  the  area  of  the  elevators  should  be  added  to  the  area  of 


DESIGN    OF   THE   CONTROL   SURFACES 


349 


the  fixed  part.  If  the  fixed  part  is  symmetrical  in  section,  the 
elevators,  in  the  case  of  a  floating  tail,  will  exert  zero  lift  when 
in  the  same  straight  line.  A  floating  tail  is  not  at  o°  angle  of 
incidence  to  the  flight  path,  but  positively  inclined  at  some 
less  angle  than  the  wings  owing  to  the  downwash,  the  rate 
of  change  of  momentum  vertically  of  which  is  the  lift  for 
horizontal  flight.  Again,  the  drag  of  the  whole  machine  is 
the  rate  of  change  of  momentum  horizontally  of  the  disturbed 
air.  Thus  the  tail  operates  in  a  region  where  the  air  is  in  a  state 
of  motion  downwards  and  forwards  relative  to  the  surrounding 


L 743'- —4 


1_  . tll... x 


Scale  of  Model  Va 


FIG.  249. — Model  of  B.E.  2  Biplane. 


atmosphere  in  gliding  flight.  It  has  been  found  experimentally 
that  the  angle  of  downwash  from  the  main  planes  is  approxi- 
mately one-half  the  angle  of  incidence  of  the  main  planes 
measured  from  the  angle  of  no  lift.  This  will  give  the  position 
of  the  tail  plane  when  '  floating.' 

Reduction  of  Effectiveness  of  the  Tail  Plane  due  to 
Wash  from  the  Main  Planes. — A  method  of  investigating 
the  effect  of  the  downwash  of  the  main  wing  surface  upon  the 
moment  exerted  by  the  tail  plane  was  to  determine  experi- 
mentally the  pitching  moment  upon  the  model  of  a  complete 
machine  for  a  large  number  of  angles  of  pitch.  The  tail  plane 
was  then  removed  from  the  model,  and  a  similar  series  of 
experiments  conducted  in  order  to  determine  the  pitching 


350 


AEROPLANE    DESIGN 


moment  on  the  model  without  its  tail  plane.  Measurements 
were  then  made  of  the  longitudinal  and  normal  forces  upon  the 
tail  plane  and  elevator  alone  at  various  angles  of  incidence.  A 
comparison  between  the  results  obtained  in  these  three  cases 
enables  the  effect  of  the  downwash  of  the  main  planes  to  be 
determined.  From  an  investigation  of  this  nature  the  N.P.L. 
found  that  both  the  normal  force  and  pitching  moment  for  the 
tail  plane  in  its  normal  position  are  reduced  approximately 
to  one-half  the  values  they  show  when  the  tail  plane  is  tested 
separately — that  is,  interference  due  to  the  downwash  from  the 
main  planes  reduces  the  slope  of  the  pitching-moment  curve 
in  this  ratio,  and  consequently  the  necessary  area  of  the  tail 


FIG.  250. — Contoured  Plan  and  Sections  for  Tail  Plane  3. 


plane  is  double  that  to  be  otherwise  expected.  These  results 
are  of  such  practical  importance  that  they  are  reproduced  here 
for  the  purposes  of  reference.  A  scale  drawing  of  the  model  is 
shown  in  Fig  249,  from  which  it  will  be  seen  that  it  is  of  the 
B.E.  type.  Experiments  were  carried  out  with  a  series  of 
different  tail  planes,  the  results  obtained  being  of  a  very  similar 
character,  those  given  here  referring  to  the  tail-plane  section 
designated  T.P.  3,  the  contours  of  which  are  shown  in  Fig.  250. 
As  will  be  seen,  this  section  is  very  similar  to  that  adopted  in 
general  practice  upon  modern  machines. 

The  effect  upon  the  value  of  the  pitching  moment  on  the 
model  of  a  change  in  the  position  of  its  CG.  was  also  observed, 
and  the  indications  showed  that  in  order  to  obtain  a  machine 
of  reasonable  longitudinal  stability  without  unduly  increasing 


DESIGN    OF   THE    CONTROL   SURFACES  351 

the  length  of  the  fuselage  and  the  area  of  the  tail  plane  it  is 
necessary  to  have  a  down  load  on  the  tail.  The  position  of  the 
C.G.  of  the  model  relative  to  the  chord  in  the  experiments  here- 
with recorded  was  at  '41  of  the  chord  from  the  leading  edge.  In 
the  first  series  of  tests  the  longitudinal  force,  normal  force,  and 
pitching  moment  were  measured  for  the  complete  machine  for 
angles  of  pitch  ranging  from  —  23°  to  +  17°  at  a  wind  speed  of 
40  feet  per  second.  These  tests  were  repeated  with  the  elevator 


x      -OB 


-•09 


-20 


FIG.  251. — Longitudinal  Force  Curves  for  Complete  Machine. 


set  at  inclinations  of  -45°.  -  30°,  -  15°,  -  10°,  -  5°,  o°,  +  5°, 
+  10°,  +15°,  +30°,  +45°,  respectively.  The  curves  corre- 
sponding to  inclination  ±  5°,  ±  10°  follow  the  general  lines  of 
o°  and  ±  15°,  and  are  omitted  for  the  sake  of  clearness.  The 
inclination  of  the  elevator  is  taken  to  be  positive  when  it  is. 
turned  downwards.  The  tail  plane  and  elevator  were  then 
removed  from  the  model  and  tested  separately  over  the  same 
angular  range  at  the  same  wind  velocity.  The  results  are  shown 
graphically  in  Figs.  251-259. 


352 


AEROPLANE    DESIGN 


•no 


•15 


OS 


N 


o 
2       o 


-OS 


Normal   Force  Curves 


for- 


45" 

30° 


0° 
I  5* 
30° 


^ 


Tad   Plane 


-20°  -15°  ~IO°  -5°  O°  -5°  to" 

Angle    of   Pitch  .  0 * 
FIG.  252. — Normal  Force  Curves  for  Complete  Machine. 


FIG.  253. — Pitching  Moment  Curves  for  Complete  Machine. 


DESIGN   OF   THE    CONTROL   SURFACES  353 


'100 


-•02 


~2O°  —  tS° 


Angle   of  Pitch   9 . 
FIG.  254. — Longitudinal  Force  Curves  for  Tail  Plane  Alone. 


FIG.  255. — Normal  Force  Curves  for  Tail  Plane  Alone. 


A  A 


354 


AEROPLANE    DESIGN 


Angle   of  Pitch    6. 

FIG.  256. — Pitching  Moment  Curves  for  Tail  Plane  Alone. 


-20'         -/J°          -to'  -5°  0'  5°  IO° 

Ang\e   of  Pitch    6  . 

FIG.  257. — Longitudinal  Force  Curves  for  Effective  Tail  Plane. 


DESIGN    OF  THE   CONTROL   SURFACES  355 


-•3 


FIG.  258. — Normal  Force  Curves  for  Effective  Tail  Plane. 


FIG.  259. — Pitching  Moment  Curves  for  Effective  Tail  Plane. 


356  AEROPLANE    DESIGN 

The  Elevator. — From  the  preceding  remarks  it  will  have 
been  observed  that  the  function  of  the  elevator  is  of  a  twofold 
.nature : 

(i.)  To  regulate  the  speed  of  flight ; 

(ii.)  To  correct  any  variation  in  the  attitude  of  the  machine 
which  may  arise  from  the  action  of  gusts  or  other 
causes. 

It  will  be  apparent  that  the  position  of  the  elevator  required 
to  maintain  equilibrium  when  the  machine  is  flying  at  its  top 
speed  will  generally  be  quite  different  from  that  required  when 
stalling.  In  addition  it  is  necessary  to  have  a  range  of  positions 
in  order  to  correct  for  disturbances  at  these  speeds,  hence  the 
maintenance  of  the  elevator  in  such  attitudes  involves  a  con- 
siderable strain  upon  tne  pilot.  Two  methods  have  been  adopted 
in  practice  to  reduce  this  strain,  namely  : 

(a]  The  elevator  is  balanced  by  means  of  an  extension  pro- 
jecting in  front  of  the  hinge  spar,  or  by  placing  the 
Binges  close  to  the  C.P.  of  the  elevator  load. 
{b)  The  function  of  the  elevator  in  regulating  the  speed  of 
flight  may  be  transferred  to  the  tail  unit  as  a  whole 
by  making  the  latter  adjustable.  This  method  is  now 
common  practice  on  most  machines,  and  reference  will 
be  made  to  it  subsequently. 

The  elevators  are  fitted  to  the  rear  of  the  tail  plane,  and 
elevate  or  depress  the  tail  of  the  machine  as  actuated  by  the 
pilot.  They  do  not  provide  the  whole  of  the  lifting  force  them- 
selves by  virtue  of  their  inclination  to  the  wind,  but  are  very 
much  more  efficient  because  they  induce  a  lift  of  like  sign  in  the 
surface  to  which  they  are  fixed,  owing  to  the  fact  that  when  rotated 
from  their  mean  position  they  form,  with  the  fixed  surface,  a 
kind  of  rudimentary  aerofoil.  The  centre  of  pressure  of  this  lift 
which  forms  the  controlling  force  is  not,  therefore,  necessarily 
upon  the  elevators  at  all :  it  may  be  somewhat  in  front  of  the 
hinge  spur.  This  does  not  mean  that  the  force  required  to  be 
exerted  by  the  pilot  for  turning  the  elevators  is  in  any  way 
diminished ;  the  distance  between  the  C.P.  of  that  part  of  the 
total  force  which  is  distributed  over  the  elevator  itself  from  the 
hinge  spar  must  be  considered  separately  in  this  connection. 
The  form  of  elevator  which  will  be  easiest  to  turn  will  be  that 
variety  which  is  not  hinged  to  a  fixed  surface;  the  total  area 
•being  sufficient  to  provide  for  the  stabilising  moments  required. 
In  this  case  the  pivot  should  be  arranged  at  the  mean  position 
•of  C.P.  travel  during  rotation. 

Owing  to  the  intervention  of  the  critical  angle,  it  is  of  no  use 
±0  arrange  for  a  greater  angle  of  incidence  being  given  to  the 


DESIGN   OF   THE   CONTROL   SURFACES  357 

elevators  than  25°,  and  even  this  amount  may  well  be  reduced. 
The  elevators  are  likely  to  be  called  upon  most  when  the  tail 
plane  itself  is  already  set,  by  reason  of  the  general  inclination 
of  the  machine,  at  a  large  angle  in  the  direction  in  which 
rotation  of  the  elevators  is  carried  out  by  the  pilot.  A  con- 
siderably smaller  rotation  than  25°  will  then  bring  about  the 
critical  angle.  In  some  cases  it  may  be  necessary  to  guard 
against  this,  as  a  considerable  fall  in  lift  may  occur  from  over- 
rotation,  a  calamity  the  cause  of  which  the  pilot  in  time  of 
emergency  cannot  be  called  upon  to  appreciate.  For  this  reason 
the  rotation  may  well  be  limited  to  between  15  and  20  degrees. 
It  is  of  course  better  to  provide  ample  surface  with  small  rotation 
than  a  meagre  surface  with  a  large  rotation.  There  is  one  great 
danger  which  must  be  guarded  against,  namely,  that  the  pilot 
should  be  able  to  exert  too  great  a  control  longitudinally.  This 
is  of  fundamental  importance  in  the  case  of  nose-diving ;  in 
which  case,  as  we  have  already  seen  in  Chapter  V.,  the  wings 
may  be  very  greatly  overstressed  if  the  pilot  should  intentionally 
or  accidentally  flatten  out  the  nose-dive  too  quickly. 


tr-T  'J K ' 


^/^yy!  }^2AL^^^^  l^-> fc 


I 

FIG.  260. — Equilibrium  of  a  Machine  in  Flight. 

Tail  Plane  Design.— From  these  experimental  results  we 
can  with  advantage  consider  their  application  to  general  design, 
and  for  this  purpose  it  is  necessary  to  draw  a  diagram  of  the 
various  forces  acting  upon  a  machine  in  normal  flight.  (See 
Fig.  260.) 

Let  A  B  represent  the  mean  chord  of 'the  wings  ; 

Xw  the  resistance  of  the  wings  ; 

Xb  the  resistance  of  the  body,  chassis,  &c. ; 

Xt  the  resistance  of  the  tail ; 

Zvv  the  normal  load  on  the  main  planes ; 

Zt  the  normal  load  on  the  tail  plane ; 

T  the  thrust  of  the  airscrew. 


358  AEROPLANE    DESIGN 

Of  these  quantities  the  mean  chord  of  a  biplane  is  determined 
in  the  following  manner.  First  find  the  length  and  position  of 
the  mean  chord  of  the  wing  surfaces,  taking  into  account  the 
variation  of  chord  over  the  surface  and  the  amount  of  the 
dihedral  angle.  Let  C  D  (Fig.  261)  represent  the  mean  chord  of 
the  top  wing  surface,  and  EF  the  mean  chord  of  the  bottom 
wing  surface. 

Join  A  E,  D  F.     Then  draw  the  line  A  B  such  that 

CA    : AE^DB : BF 

_  effective  area  of  bottom  plane 
effective  area  of  top  plane 

the  effective  areas  of  the  top  and  bottom  planes  being  deter- 
mined as  shown  in  Chapter  III.  This  mean  chord  represents 
the  chord  of  an  imaginary  monoplane  surface  equivalent  aero- 
dynamically  to  the  several  planes  of  a  multiplane. 


FIG.  261.—  Equivalent  Chord.  FIG.  262. 

The  values  of  the  resistances  of  the  wings  and  tail  are  easily 
determined  from  a  knowledge  of  their  aerodynamic  characteristics. 
The  resistance  of  the  body  and  the  point  at  which  its  resultant 
may  be  taken  to  act  is  determined  by  summing  up  the  resistance 
of  the  various  components  included  for  a  given  speed,  as  shown 
in  Chapter  XIII.  By  taking  moments  of  the  various  resistances 
about  some  fixed  point,  the  position  of  the  resultant  is  found. 
The  airscrew  thrust  at  any  speed  is  determined  from  particulars 
of  the  airscrew  which  is  to  be  used.  The  normal  force  on  the 
wings  can  be  calculated  from  the  wing  characteristics  and  the 


•t> 
area. 


Now  taking  moments  about  the  C.G.  of  the  machine  (see 
Fig.  260) 

Zt  (I  -  t)  =  Zw  (a  -  b)  +  T/-  (X*d  +  Xbf  +  Xtg) 

Formula  98 


DESIGN    OF   THE    CONTROL   SURFACES  359 

This  formula  gives  the  requisite  moment  to  be  exerted  by 
the  tail  plane  to  secure  equilibrium.  By  substituting  the  values 
of  the  quantities  for  the  range  of  speeds  over  which  the  machine 
is  required  to  operate,  a  series  of  tail  moments  are  obtained, 
from  which  it  is  possible  to  choose  the  tail-plane  area  and 
setting  which  will  best  satisfy  the  given  conditions. 

The  moments  set  up  by  the  'tail  plane  when  the  machine  ib 
disturbed  from  its  position  of  equilibrium  must  be  such  that 
they  always  tend  to  restore  the  position  of  equilibrium,  but  for 
ease  of  control  it  is  essential  that  the  righting  moments  should 
be  comparatively  small  with  small  displacements  from  the 
position  of  equilibrium,  while  they  should  increase  with  increase 
of  displacement. 

It  is  necessary  in  deciding  on  the  size  of  tail  plane  required 
for  a  given  machine  to  consider  it  in  conjunction  with  the  length 
of  the  fuselage.  As  will  be  seen  subsequently  in  relation  to  the 
rudder,  there  is  an  advantage  in  a  fairly  long  distance  between 
the  C.G.  of  the  machine  and  the  tail ;  but  for  stabilising  quality 
of  the  tail  plane,  moment  only  is  of  importance.  A  curve  may 
be  drawn  representing  the  moments  of  lift  of  wings  at  various 
angles  of  incidence — owing  to  the  travel  of  the  centre  of 
pressure — about  the  C.G.  of  the  machine,  assuming  the  machine 
to  swing  while  in  a  straight  path  under  its  inertia.  A  similar 
curve  will  show  the  correcting  couples  due  to  the  change  cf 
angle  of  the  tail.  The  first  curve  may  be  subtracted  geomet- 
rically from  the  second,  and  thus  may  be  obtained  a  righting 
couple  curve  which  is  an  index  to  the  statical  stability  of  the 
machine. 

Determination  of  Dimensions  of  the  Tail  Plane  and 
Settings  of  the  Elevator.— In  the  following  paragraphs  the 
design  of  a  tail  plane'is  fully  carried  out,  since  it  is  only  by  such 
a  method  that  the  nature  of  the  problem  involved  can  be  fully 
understood  and  grasped.  The  machine  for  which  this  tail  unit 
is  designed  will  be  the  one  for  which  the  wing-bracing  stresses 
were  worked  out  in  Chapter  V.,  the  weight  being  2000  Ibs.,  the 
effective  area  of  the  supporting  surfaces  366  square  feet,  and  the 
wing  characteristics  those  given  in  Table  XLIX.  The  C.G.  of  the 
machine  is  assumed  to  be  at  "32  of  the  chord  from  the  leading 
edge  of  the  wing,  the  distance  between  the  C.G.  of  the  machine 
and  the  centre  of  pressure  of  the  tail  being  16  feet.  The 
tail-plane  section  to  be  used  will  be  the  T.P.  No.  3,  for  which 
the  contours  arc  given  in  Fig.  250.  The  chord  of  the  wing 
is  6  feet,  and  the  angle  of  incidence  relative  to  the  body  axis 
is  4°. 


360  AEROPLANE    DESIGN 

TABLE  XLIX.  —  WING  CHARACTERISTICS. 

Inclination  of  wing  to  wind    ...  o°  2°  4°  63 

Absolute  lift  coefficient  (Ky)  ...  0*09  0*205  0-298  0-37 

Pos11  of  C.  P.  (fraction  of  chord)  °'575  °'425  °'35^  °'329 
Pos11  of  C.P.  relative  to  C.G. 

chord  (—  behind,  +  in  front)  -0*255  -  0*105  -0-038  -0*009 

Ditto  (feet)          ......      -i'53        -0^63       -0-228      -0-054 

Pitching  moments  (Ibs.  ft.)    ...      -3060       -1260       -456         -  108 

Inclination  of  wing  to  wind    ...  8°  10°  12°  14° 

Absolute  lift  coefficient  (Ky)  ...         0-441         0-514         0-573         0-598 
Pos11  of  C.P.  (fraction  of  chord)         0-312         0-302         0-292         0*28 

Pos11  of  C.P.  relative  to  C.G. 
chord  (-  behind,  +  in  front)     +0-008     +  0-018     4-0-028     +0-04 

Ditto  (feet)  ......      +0-048      +0-108     +0-168      +0-24 

Pitching  moments  (Ibs.  ft.)    ...      +96  +216         +336         +480 

The  normal  force  on  the  wing  may,  with  sufficient  accuracy, 
be  assumed  to  be  equal  to  the  weight  of  the  machine.  The  small 
variation  in  the  load  due  to  the  tail-plane  pressure  is  also 
ignored.  The  pitching  moments  on  the  machine  due  to  the 
travel  of  the  C.P.  are  shown  in  Table  XLIX. 

The  function  of  the  tail  plane  is  to  introduce  opposing 
moments  to  these,  so  that  the  total  pitching  moment  upon  the 
machine  in  normal  flight  is  zero.  Other  forces  besides  the 
wings  and  the  tail  plane  modify  the  pitching  moment  on  a 
machine,  as  is  seen  by  reference  to  Fig.  260  ;  but,  for  the  sake 
of  simplicity  and  clearness,  these  will  be  neglected  in  the  present 
case.  In  an  actual  design,  however,  they  must  not  be  ignored, 
and  each  of  the  forces  shown  must  be  considered. 

It  is  therefore  assumed  that  the  C.G.  of  the  machine  lies  along 
the  mean  chord  of  the  wings,  and  that  the  line  of  thrust  and 
body  and  wing  resistance  passes  through  the  C.G.  Hence  c,  d,f,g 
in  Formula  98  are  each  equal  to  zero,  so  that  the  only  forces 
producing  a  pitching  moment  upon  the  machine  are  the  normal 
forces  upon  the  wings  and  the  tail  plane  respectively. 

Moment  due  to  the  tail  =  Normal  force  on  tail  x  distance  of  tail  C.P. 
from  C.G.  of  machine 

y  P  A'  V2  / 


g 


DESIGN   OF   THE   CONTROL  SURFACES  361 

Where     6'  =  angle  of  incidence  of  tail  plane  to  relative  wind 
A'  =  area  of  tail  plane 

y  =  rate  of  change  of  normal  force  on  tail  plane  with  angle 

^  0  of  incidence. 

/  =  distance  from  C.P.  of  tail  plane  to  C.G.  of  machine. 

From  the  experiments  on  the  tail  plane  No.  3  it  was 
observed  that  the  angle  of  downwash  from  the  main  planes  is 
approximately  one-half  the  angle  of  incidence  of  the  main 
planes  measured  from  the  no  lift  position.  This  for  the  section 
employed  is  —  2°,  so  that  the  following  table  can  be  prepared  : — 

TABLE  L. 

Inclination  of  wings  to  wind  ...     o°  2°     4°     6°       8°     10°     12°     14° 
Inclination  of  wings  measured 

from  angle  of  no  lift  ...     2°  4°     6°     8°     10°     12°     14°     16° 

Angle  of  downwash      ...         ...     i°  2°     3°     4°       5°       6°       7°       8° 

At  this  stage  it  is  necessary  to  determine  A'  and  9'  by  trial. 
A  value  of  'A'  must  be  assumed  and  the  necessary  tail  setting  Br 
calculated  as  in  the  following  manner.  If  the  result  obtained 
by  this  assumed  value  is  unsatisfactory,  a  fresh  value  for  A'  must 
be  taken,  and  the  calculations  repeated  until  a  satisfactory 
setting  results.  In  this  connection  it  is  very  useful  to  refer 
to  some  such  table  as  that  given  on  page  439,  in  which  the 
dimensions  of  the  tail  plane  for  several  successful  machines  are 
shown.  From  this  table  an  estimate  can  be  formed  in  most 
cases  of  a  probable  suitable  size.  A  tail  plane  of  span  16  feet 
and  a  chord  4  feet  will  be  assumed  for  the  tail  plane  under  con- 
sideration. Two  cases  will  be  considered  : 

(a)  A  tail  plane  of  variable  angle  of  incidence  relative  to  the 

body  axis. 

(b)  A  tail  plane  of  fixed  angle  of  incidence  relative  to  the 

body  axis. 

(a)  In  this  method,  by  adjusting  the  angle  of  incidence  of  the 
complete  unit,  equilibrium  at  varying  speeds  of  flight  is  obtained 
without  the  use  of  the  elevator,  the  latter  being  used  solely  to 
perform  corrective  manoeuvres  about  the  position  of  equilibrium. 

Moment  due  to  tail  =  6'  — -/  x  -00237  x  64  V2  x  16 
d  0 

By  reference  to  the  curves  shown  in  Fig.  255,  it  will  be  seen 
that  the  normal  force  on  the  tail  plane  increases  with  the  angle 


362  AEROPLANE    DESIGN 

of  incidence  according  to  a  straight-line  law  and  the  value  of 
the  slope 

dZ 


This  refers  to  the  model  of  area  '1275  square  feet  at  a  wind 
.speed  of  40  feet  per  second 

'*'      °158  =  ~df  X  <00237  x  'I275  x  4°~ 

whence  --  £  =  -033 

dff 

that  is,  the  rate  of  change  of  the  absolute  lift  coefficient  for  the 
Tail  Plane  Section  No  3  when  interference  effects  are  absent  is 
•033.  Interference  effects  reduce  this  figure  by  approximately 
one-half.  Hence  we  may  write  the  moment  due  to  the  tail 

=  0'  x  -Jz5  x  -00237  x  64  x  16  V2 


-  -o4  0'  V2 
Also       V'2  = 


W  2000 


Ky       X         -00237        X        366 


From  the  values  given  by  the  relationships  A  and  B  a  table 
of  the  following  nature  can  be  prepared  : 

TABLE  LI. 


Angle  of 
incidence 
of  wing. 

V2                 Moment  due 
to  tail. 

Moment             ^ 
required. 

V  = 

oment  required 

Moment 

o°       ... 

25600 

1024  ft' 

-   3060 

3 

2° 

II2OO 

4480'       ... 

-    1260 

-  2-82 

4°       .-. 

7740      ... 

310^'      ... 

456        ... 

-  1-47 

6°       ... 

6220 

249  6'      ... 

1  08 

-  0-43 

8°      ... 

5200 

208  6'      ... 

+        96 

+  0-46 

10°         ... 

4480      ... 

179  V      ... 

+      216 

-f    I'2 

12° 

4020      ... 

161  0'      ... 

+      336        ... 

+  2-08 

14°      ... 

3850      .•• 

1560'      ... 

+     480 

+  3'oS 

DESIGN   OF   THE   CONTROL   SURFACES  363 

The  angle  of  the  tail  plane  relative  to  the  downwash  of  the 
•machine  must  therefore  vary  between  —  3°  and  +  3°.  The  angle 
required  for  determining  the  travel  of  the  variable  gear  is  that 
relative  to  the  body  axis.  The  angle  of  the  body  axis  is  4°  less 
than  that  of  the  wings,  whence  Table  LI  I.  can  be  prepared 
from  Tables  L.  and  LI. 

TABLE  LI  I. 

Angle  of  wing  to  wind          ...          ...  o°  2°  4°  6° 

Angle  of  body  axis    ...          ...          ...  -4°  -2°  o°  2° 

Angle  of  downwash  relative  to  body 

axis  -5°  -4°  -3°  -2° 

Angle  of  tail  plane  relative  to  bo  iy...  2-0°  i'i8°  i'53°  r'57* 

Angle  of  wing  to  wind          ...         ...  8°  10°  12°  14° 

Angle  of  body  axis :.  4°  6°  8°  10° 

Angle  of  downwash  relative  to  body 

axis           ...          ...          ...          ...  -  i°  o°  i°  2° 

Angle  of  tail  plane  relative  to  body...  1-46°  1-2°  1-08°  1-08° 

It  is  thus  seen  that  a  variation  in  the  angle  of  incidence  of 
the  tail  plane  and  elevator  relative  to  the  body  axis  of  from 
+  2°  to  +  i°  is  sufficient  to  ensure  equilibrium  at  all  angles  of 
flight  with  no  deflection  of  elevator  relative  to  the  tail  plane. 
Examples  of  Tail  Plane  Incidence  Gears  are  shown  in  Figs. 
274  and  275. 

(b)  Tail-plane  setting  fixed  relative  to  the  body.  With  this 
method  equilibrium  at  various  speeds  is  obtained  by  the  use  of 
the  elevator.  It  is  therefore  necessary  to  choose  some  inter- 
mediate position  for  the  tail-plane  setting  in  order  that  the 
requisite  elevator  deflection  may  be  small,  thereby  ensuring  that 
sufficient  additional  moment  may  be  secured  for  manoeuvring. 

From  an  examination  of  the  tail-plane  settings  in  the  case 
just  considered  it  is  probable  that  a  fixed  angle  of  incidence  of 
i  J°  relative  to  the  body  will  be  suitable.  Using  this  figure  the 
angle  of  downwash  relative  to  the  tail  plane  is  as  shown  in 
Table  LIII. 

TABLE  LIII. 

Angle  of  incidence  of  wings      ...          o°  2°  4°              6° 
Angle  of  downwash  relative  to  tail 

planed'         ~  3i°  ~  2i°  ~  Ti°  ~  i° 

Moment  due  to  tail  plane          ...  -3590  -1120  -464  -124 

Moment  required            ...          ...  -3060  -1260  -456  -  108 

Moment  to  be  exerted  by  elevator  +530  140  +8  +    16 


364  AEROPLANE   DESIGN 

Angle  of  incidence  of  wings       ...          8C  10°  12°  14° 

Angle  of  downwash  relative  to  tail 

plane  6'          ...         ...         ...  \"  ij°  2^°         3^" 

Moment  due  to  tail  plane          ...  +    108  +   358  +402  +540- 

Moment  required  ...          ...  +      96  +    216  +336  +480 

Moment  to  be  exerted  by  elevator  12  142  66  -    60 

Additional  Moment  due  to  Deflection  of  Elevator- 
Referring  to  Fig.  255  it  will  be  seen  that  the  increase  in 
normal  force  due  to  the  deflection  of  the  elevator  at  a  fixed 
angle  of  pitch  is  approximately  proportional  to  the  angle  of 
deflection  over  the  range  of  angles  of  pitch  from  —  11°  to  -f  5°. 
On  plotting  this  increase  of  normal  force  the  variation  of  lift 
coefficient  for  the  section  per  degree  movement  of  elevator  is 
found  to  be  *oi8.  Allowing  a  decrease  of  50%  due  to  its  opera- 
tion in  the  downwash  of  the  main  planes,  a  value  of 


is  deduced.     Hence  the  increase  of  normal  force  on  the  tail  due- 
to  the  deflection  Q"  of  the  elevator 

=  6"  x  '009  x  -00237  x  64V2 
whence  additional  moment 

=  -0219  V20" 

and  the  required  deflection  of  elevator  at  each  speed  in  order  to 
produce  equilibrium 

fl"  =  Moment  to  be  exerted  by  elevator 

•0219  V2 
.*.  6"  =   +  o'95°   -  o'57°  +  o°  +  o'i2°  -  o-io  -  1*45°  —  075  -  0*70° 

It  will  be  seen  that  the  deflection  of  elevator  required  for 
equilibrium  is  almost  negligible  when  a  correct  tail-plane  setting 
has  been  secured.  Consequently,  in  a  case  such  as  the  present 
no  advantage  is  to  be  derived  by  installing  a  tail-incidence  gear, 
such  a  device  being  generally  of  more  value  in  the  case  of  large 
machines. 

So  far  the  method  of  design  has  been  limited  to  the  deter- 
mination of  the  righting  moments  necessary  to  produce  equili- 
brium at  a  particular  angle  of  incidence.  Before  finally  deciding 
upon  the  tail  plane  it  is  essential  to  examine  whether  equilibrium 
will  be  restored  should  the  machine  be  temporarily  deflected 
from  its  normal  flight  attitude  by  a  gust  or  other  cause.  For 
stable  equilibrium  it  is  necessary  that  the  moments  set  up  by 


DESIGN   OF   THE   CONTROL   SURFACES  365 

the  tail  plane  in  the  event  of  such  disturbance  are  sufficient  to 
overcome  the  unbalanced  moment  set  up  by  the  wings  and  to 
.restore  the  machine  to  its  original  flight  attitude.  For  such  to 
be  the  case,  the  moment  due  to  the  tail  plane  must  increase  at  a 
faster  rate  than  that  due  to  the  wings.  Now,  from  Fig.  260 

Moment  due  to  wings  -  Ky  £  A  V2  (a  -  b) 

o 

and  Moment  due  to  tail       =  K'y  £  A'  V2  / 

Since  p/g  (V2)  is  common  to  both  expressions,  it  follows  that  the 
moment  due  to  the  wings  is  proportional  to  Ky  A  (a  —  b)  and 
the  moment  due  to  the  tail  proportional  to  K'y  A'  /.  By  plotting 
these  exnressions  on  a  pitch-angle  base,  curves  such  as  are 
shown  in  Figs.  263  and  264  result,  and  an  examination  of  such 
curves  enables  conclusions  to  be  drawn  as  to  the  probable 
dynamic  stability  of  the  machine. 

For  the  machine  previously  considered,  the  values  for  Ky  A 
(a  —  b}  for  different  wing  angles  are  shown  in  Table  LIV.,  and 
for  the  tail  plane  the  values  of  K'y  A'  /  are  shown  in  the  same 
table,  where 


v  -  • 

dtf 
for  fixed  angles  of  ij°  to  body. 


Incidence  of  wings 


TABLE  LIV, 

0° 

2° 

4° 

6° 

•c9 

•205 

•298 

'37 

••      -i'53 

-'63 

-•228 

•054 

..      -5°'4 

-47  '4 

-24-9 

•    7'3 

KyA  (a-b)  x  366  ... 

Angle  of  tail  plar  e  relative  to 
downwash  0' 

K'y  =  0'  x  -0165  

K'y  x  1 6  x  64 

Incidence  of  wings  


Ky A(a-t>)  x  366  ... 

Angle  of  tail  plane  relative  to 

downwash  0'  ...          ...  J°  ij°  2^°          3^° 

K'y  =  0'  x  '0165        ...         ...         '0082         '0248         '0413         '0578 

K'y  x  16  x  64  -8-4          -25-4        -42*3        -59*2 


-35° 

-  22° 

-  i  J° 

-r 

-•0578 

-  -0413 

-  '0248 

-  "0082 

59'2 

42-3 

25'4 

8-4 

8° 

10° 

12° 

14° 

•442 

•5i4 

'573 

•598 

•048 

•108 

•168 

•24 

7-76 

20-3 

35*2 

52*5 

366 


AEROPLANE    DESIGN 


These  values  are  shown  plotted  in  Fig.  263.  The  moment 
due  to  the  tail  plane  is  a  straight  line,  whose  position  may  be 
shifted  (corresponding  to  a  movement  of  the  elevator)  such  that 
equilibrium  may  be  obtained  at  each  angle  of  incidence  of  the 
wings.  The  slope  of  the  resultant  curve  obtained  by  combining 
the  two  curves  will  indicate  the  nature  of  the  equilibrium  at  the 
various  attitudes  of  flight. 

These  curves  are  shown  in  Fig.  263,  and  it  will  be  observed 


Case  I .    A'  =  64  sQ.fr. 
I  -   16  fh_ 

I 
WingCoeff. 


FIG.  263.— Case  I. 

that  the  slope  of  the  resultant  curve  for  which  equilibrium  is 
obtained  at  angles  of  from  5°  to  I2C  is  of  opposite  sign  to  that 
for  angles  2°  to  5°.  Between  angles  of  5°  to  12°  the  equilibrium 
is  such  that  an  alteration  in  the  angle  of  incidence  of  the  wings 
sets  up  a  pitching  moment  which  causes  the  machine  to  revert  to 
its  original  position — that  is,  the  equilibrium  is  stable.  Between 
angles  2°  to  5°  an  alteration  in  attitude  of  the  machine  sets  up  a 
pitching  moment  which  tends  to  increase  the  deviation  from  the 


DESIGN   OF   THE   CONTROL   SURFACES 


367 


equilibrium  position,  hence  the  equilibrium  is  unstable,  and 
unless  a  correcting  moment  is  introduced  by  a  movement  of  the 
elevator,  the  attitude,  and  consequently  the  speed,  will  be  per- 
manently altered.  It  is  therefore  apparent  that,  to  secure  stable 
equilibrium  at  all  angles  of  incidence,  the  slope  of  the  curve  due 
to  the  tail  plane  must  at  all  points  be  greater  than  that  of  the 
curve  due  to  the  wings.  The  slope  of  the  tail-plane  curve  is 
directly  proportional  to  the  area  of  the  tail  A',  and  the  length 


-60 


ng  Coeff 


FIG.  264.— Case  II. 

from  the  C.G.  at  which  it  is  acting  (/) ;  therefore  by  increasing 
either  of  these  factors  stable  equilibrium  can  be  secured  in  the 
above  case.  For  the  present  purpose  an  increase  in  /  from  1 6  to 
20  feet  will  be  adopted.  The  values  of  K'y  A'  /  will  then  be 
as  shown  in  Fig.  264.  In  this  case  the  equilibrium  is  stable 
throughout  the  complete  range,  of  flying  angles. 

In  actual  design  work  this  latter  operation  must  be  carried 
out,  before  determining  the  tail  settings,  otherwise  in  the  event 


368 


AEROPLANE    DESIGN 


of  any  alteration  in  the  main  dimensions  being  necessary,  as 
was  the  case  in  this  example,  the  whole  of  the  preceding  work 
would  have  to  be  repeated.  The  order  in  the  present  chapter 
is  due  to  reasons  of  clarity,  it  being  easier  to  understand  the 
principles  involved  after  the  treatment  of  the  tail  settings. 

Having  thus  secured  a  tail  plane  to  give  stable  equilibrium 
at  all  speeds,  an  investigation  into  the  longitudinal  stability  of 
the  machine  should  be  carried  out  according  to  the  method 
shown  in  Chapter  X.  A  satisfactory  result  will  in  all  pro- 
bability be  secured,  and  the  dimensions  of  the  tail  plane  can 
then  be  embodied  in  the  general  design  of  the  machine. 

Fin  and  Rudder. — The  fin  and  rudder  form  the  stabilising 
and  control  surfaces  for  directional  flight.  In  certain  cases  the 


Scale  of  Model  io. 


FIG.  265  —Model  of  S.  E.  4  Body. 


rudder  may  be  used  without  a  fin,  and  under  these  circum- 
stances it  performs  the  dual  function  of  a  stabilising  and  con- 
trolling surface.  Such  an  arrangement,  however,  should  be 
limited  to  small  machines.  On  rotation  of  the  machine  about 
the  axis  of  yaw,  the  rudder  and  fin,  together  with  all  members  of 
the  aeroplane  which  present  a  side  area  to  the  line  of  flight 
upon  rotation,  produce  a  horizontal  force  transverse  to  the  line 
of  flight  which  is  known  as  the  lateral  force. 

Just  as  curves  can  be  drawn  for  longitudinal  '  static '  stability, 
so  also  can  curves  be  drawn  in  the  case  of  members  contributing 
lateral  force  during  or  owing  to  directional  change  ;  the  moments 
of  lateral  forces  about  the  C.G.  of  the  machine  being  plotted. 
The  rudder,  and  fin  if  any,  must  then  be  sufficiently  large  to 
ensure  that  there  is  always  a  small  positive  residual  moment — 


DESIGN  OF  THE  CONTROL  SURFACES 


369 


that  is,  a  moment  which  tends  to  restore  the  machine  to  its 
proper  direction.  The  balance  should  be  right  in  the  case  of  a 
tractor  machine  when  the  engine  is  working,  as  then  the  pro- 
peller exercises  more  fin  effect  than  in  gliding  flight.  Lateral 
force  is  to  be  avoided  as  far  as  possible,  owing  to  the  fact  that 
it  produces  side  slip.  For  this  reason,  therefore,  a  long  fuselage 
carrying  a  small  rudder  is  an  advantage.  The  same  remarks  as 
were  made  in  reference  to  the  elevators  are  applicable,  but  to  a 
less  extent,  owing  to  the  smaller  area,  with  regard  to  the  inter- 
action of  the  rudder  and  fin.  The  rudder  may  with  advantage 
be  given  a  moderate  amount  of  aspect  ratio,  particularly  in  the 
case  where  there  is  no  fin. 


-20° 


-5°  O" 

Angle   of  Yaw 


FIG.  266. — Yawing  Moment  on  Model  of  S.  E.  4  body. 


Wherever  possible,  the  lateral  force  on  a  machine  should  be 
deduced  from  experiments  on  a  model  of  the  machine  being 
designed.  An  example  of  the  experimental  determination  of 
the  lateral  force  and  yawing  moment  upon  a  model  is  shown  in 
Figs.  266  and  267. 

The  model  was  of  the  S.  E.  4  body,  and  was  one-tenth  full 
size,  the  overall  length  with  rudder  in  position  being  25".  This 
model  is  shown  in  Fig.  265.  Measurements  of  the  lateral  force 
and  yawing  moment  about  the  C.G.  of  the  machine  were  made 
for  four  modifications  of  the  model,  namely  : 

(a)  With  fins  and  rudder  straight. 

(b)  With  rudder  set  over  at  10°. 
(c}   With  fins  on  and  rudder  off. 
(d)  Without  fins  and  rudder. 

B  B 


AEROPLANE    DESIGN 

The  curves  (a),  (£),  (d)  in  all  figures  show  the  progressive 
effect  of  the  decrease  of  rudder  and  fin  area.  The  lateral  force 
is  reduced  to  about  70%  of  its  value  by  removing  the  rudder,  and 
to  about  40%  of  its  value  by  removing  fins  as  well  The  yawing 
moment  is  reduced  to  about  35%  by  removing  the  rudder,  and 
changes  sign  when  the  fins  are  also  taken  off,  showing  that  the 
body  is  unstable  as  regards  yawing  about  the  C.G.  when  there 
is  no  fin  area  at  the  after~end. 

In  the  event  of  such  experimental  information  being  unob- 


-25°     -so0     -13°      -10°      -5° 


£0°         £5 


FIG.  267. — Lateral  Force  on  Model  of  S.  E.  4  body. 


tainable  for  a  machine  under  design,  the  following  figures  may 
be  used  : — 


TABLE  LV. 


ITEM. 

Streamline  wires 
Streamline  struts 
Fuselage 
Rudder  and  fin 


Lateral  Force  in  Ibs.  per  Degree 
Yaw  at  100  f.p.s. 

o'8  Ibs.  per  square  foot  side  area. 
07  Ibs.  per  square  foot  side  area, 
o'n  Ibs  per  square  foot  side  area. 
0*6  Ibs.  per  square  foot  side  area. 


Landing  chassis  and  Wheels  ...     0*8  Ibs.  per  square  foot  side  area. 

From  a  side  elevation  of  the  machine  the  amount  of  side 
area  presented  by  the  various  members  may  be  assessed  and  the 
lateral  force  then  calculated. 


DESIGN    OF   THE   CONTROL    SURFACES  371 

Lateral  Force  due  to  the  Airscrew. — When  investigating 
the  lateral  stability  of  the  B.E.  2  machine  it  was  found  experi- 
mentally that  the  total  side  force  upon  the  machine  when  the 
airscrew  was  rotating  was  considerably  greater  than  a  calcula- 
tion of  the  known  lateral  forces  had  indicated.  This  led  to  an 
investigation  of  the  possible  action  of  the  airscrew  as  a  fin,  and  a 
mathematical  theory  was  developed  by  Mr.  T.  W.  K.  Clarke,  B.A., 
A.M.I.C.E.,  from  the  following  considerations.  Referring  to  Fig. 
268,  it  will  be  seen  that  the  effect  of  a  side  wind  will  be  to  cause 
a  difference  in  the  velocity  of  the  airscrew  blades  relative  to  the 
air  according  as  to  whether  they  are  moving  in  the  direction  of 
the  side  wind  or  moving  towards  it — that  is,  if  u  be  the  velocity 
of  the  side  wind,  and  v  the  velocity  of  the  blade,  then  the 
velocity  of  the  blade  relative  to  the  wind  will  be  v  —  u  and 
v  +  u  respectively.  The  result  of  this  will  be  that  the  angle  of 


FIG.  268. — Lateral  Force  on  Airscrew. 

attack  for  the  lower  blade  will  be  increased  (see  Chap.  IX.), 
while  that  for  the  upper  blade  will  be  diminished.  This  increase 
in  the  angle  of  attack  and  the  increased  velocity  of  the  lower 
blade  relative  to  the  air  produce  a  greater  pressure  on  the  lower 
blade,  while  upon  the  upper  blade  there  is  a  decrease  in  pres- 
sure :  hence  the  side  components  of  the  forces  on  the  blades  no 
longer  balance  each  other,  and  it  is  this  unbalanced  force  which 
causes  the  variation  of  total  side  force  according  as  the  airscrew 
is  rotating  or  motionless  relative  to  the  machine. 

An  experimental  verification  of  the  theory  was  carried  out 
by  the  N.P.L.,  and  it  was  found  that  the  results  were  in  good 
agreement  with  those  calculated.  For  an  airscrew  of  9  feet 
diameter  and  speed  of  900  r.p.m.,  such  as  was  used  on  the 
B.E.  2,  the  lateral  force  was  found  to  be  io-3  Ibs.,  with  an  angle 
of  yaw  of  5°  and  a  translational  speed  of  100  f.p.s.  For  angles 
up  to  25°  the  force  is  approximately  proportional  to  the  angle 
of  yaw. 

After   an    estimate  of  the  lateral  force  per  degree  of  yaw 


372  AEROPLANE    DESIGN 

upon  the  various  members  of  a  machine  has  been  made, 
the  yawing  moment  about  the  C.G.  can  be  determined,  it 
being  the  sum  of  the  various  lateral  forces  multiplied  by  their 
respective  distances  from  the  C.G.  This  calculation  will  en- 
able the  f  minimum  '  size  of  fin  and  rudder  area  required  to 
give  directional  stability  to  be  estimated.  The  maximum  size 
of  fin  is  fixed  by  considerations  relating  to  spiral  instability, 
as  was  indicated  in  Chapter  X.  The  condition  for  spiral 
instability  there  stated  was  that  the  numerical  value  of  the 
ratio  of  the  derivatives  LV/NV  should  be  greater  than  the  ratio 
of  the  derivatives  Lr/Nr.  The  limiting  condition  for  stability 
will  therefore  be  reached  when 


= 

Lr      Nr 

and  this  will  give  a  value  for  the  maximum  fin  permissible. 
The  value  of  Lv  is  dependent  upon  the  dihedral  angle  of  the 
machine,  and  hence  this  forms  the  readiest  means  of  securing 
spiral  stability,  as  in  most  cases  it  is  simpler  to  assume  a  size  of 
fin  by  reference  to  successful  machines  of  a  similar  size.  The 
dihedral  angle  can  then  be  varied,  if  necessary,  to  give  the 
required  degree  of  stability.  The  determination  of  the  above 
derivatives  necessitates  model  experiments  for  the  best  results, 
though  in  the  absence  of  such  data  they  may  be  calculated  to  a 
fair  degree  of  approximation  in  the  manner  shown  in  Chapter  X. 

Ailerons  or  Wing  Flaps.  —  Control  about  the  axis  of  roll 
is  provided  generally  by  means  of  hinged  ailerons  or  flaps.  In 
the  early  stages  of  aviation  the  method  of  warping  the  wings 
was  adopted,  but  this  practice  has  now  been  almost  abandoned. 
When  dealing  with  the  elevator,  it  was  stated  that  the  effect  of 
rotating  the  elevator  with  reference  to  the  tail  plane  was  to 
increase  or  decrease  the  lift  of  the  combined  surface.  In  the 
case  of  the  aileron  a  continuous  high  lift/drag  ratio  is  of  prime 
importance.  The  angle  of  rotation  must  therefore  be  small  and 
the  flaps  consequently  large. 

In  actual  practice  we  find  a  wide  range  of  aileron  areas 
according  to  the  width  and  the  amount  of  rotation  employed. 
The  moment  required  depends  upon  the  span,  the  area  of  the 
wings,  and  the  transverse  moment  of  inertia  of  the  whole 
machine.  The  area  itself  also  depends  upon  the  speed  and  the 
speed  range.  In  designing  the  ailerons,  attention  must  be  paid 
to  the  yawing  moments  induced  by  using  the  flaps.  We  have 
previously  seen  that  a  reflexed  trailing  edge  diminishes  the 
resistance  of  a  wing.  If  the  flaps  are  interconnected,  therefore 


DESIGN    OF   THE   CONTROL   SURFACES 


373 


the  resistance  of  one  wing  will  be  diminished  while  that  of  the 
other  is  increased,  thus  necessitating  simultaneous  use  of  the 
rudder.  When  the  rudder  is  used  to  produce  a  turning  move- 
ment, banking  is  necessary  to  prevent  side-slip.  If  the  machine 
be  banked  by  use  of  ailerons  or  warping  of  the  wings,  the  upper 
wing-tip  will  have  the  flap  pulled  down  and  so  will  have  an 
increased  resistance  ;  while  the  reverse  is  the  case  for  the  lower 
wing-tip.  But  the  upper  wing-tip  is  required  to  travel  faster 


•3  -4  -5  -6 

Lift   Coefficient    (Absolute) 

FIG.  269. — Comparison  of  Lift  Drag  Rated  for  Aerofoil 
with  and  without  Flaps. 

than  the  lower  one,  and  thus  the  rolling  control  opposes  the 
rudder  action.  In  an  extreme  case  the  size  of  the  rudder  might 
have  to  be  increased  to  take  account  of  this. 

Experiments  relating  to  an  aerofoil  with  a  hinged  flap  are 
described  in  the  1913-1914  Report  of  the  Advisory  Committee 
for  Aeronautics.  Although  these  experiments  were  not  made 
in  connection  with  the  question  of  aileron  surface,  they  are  of 
considerable  interest  in  this  respect,  and  therefore  the  most 
important  results  are  here  given.  The  section  of  the  aerofoil 
used  in  these  experiments  was  similar  in  form  and  aerodynamic 


374 


AEROPLANE    DESIGN 


characteristics  to  that  shown  in  Wing  Section  No.  6.  The 
dimensions  were  18"  by  3",  and  the  flap  extended  over  the 
whole  length  of  the  rear  part  of  the  section,  being  1*155"  wide 
(•385  chord).  The  gap  in  the  aerofoil  due  to  the  hinges  was 
rilled  with  plasticine,  as  it  was  found  .that  the  drag  was  greater 
if  this  was  not  done.  Angles  of  pitch  were  in  all  cases  measured 
from  the  chord  of  the  original  aerofoil,  so  that  when  the  flap 
angle  was  zero  the  section  corresponded  exactly  with  that 
shown  in  Fig.  72. 

Fig.  269  represents  the  value  of  the  L/D  ratio  plotted 
against  lift  coefficient  for  the  most  efficient  equivalent  aerofoil 
— that  is,  the  combination  of  angle  of  incidence  of  chord  with 


FIG.  270. — Movement  of  C.P.  for  Aerofoil  with  Hinged  Flap 
compared  with  Original  Aerofoil. 

angle  of  flap  to  give  maximum  efficiency  as  compared  with  the 
original  section.  The  angle  of  pitch  of  the  wing  and  the 
relative  pitch  for  the  flap  are  marked  on  the  figure,  and  the 
corresponding  curve  with  zero  angle  of  pitch  of  flap  are  shown 
on  the  same  figure.  In  the  neighbourhood  of  points  of  greatest 
efficiency  it  will  be  noticed  that  an  alteration  of  flap  angle  gives 
a  better  lift  without  alteration  of  the  pitch  angle  of  the  wing 
itself,  while  maximum  lift  is  obtained  with  the  flap  at  a  large 
angle  of  pitch  and  the  incidence  of  the  wing  itself  smaller  than 
at  the  corresponding  point  for  the  original  section.  The  centres 
of  pressure  for  these  most  efficient  combinations  are  shown  in 
Fig.  270.  For  values  of  lift  coefficient  between  '13  and  '3  the 
C.P.  moves  backward  with  increase  of  lift  coefficient.  The 
equivalent  aerofoil  is  therefore  stable  over  the  most  important 


DESIGN    OF   THE   CONTROL   SURFACES  375 

portion  of  the  range  of  lift  coefficient  used  at  ordinary  flying 
speed . 

From  these  experiments  the  following  important  conclusions 
as  to  the  advantages  of  using  a  wing  with  a  hinged  rear  portion 
can  be  deduced  : 

1.  That   the   increased    maximum    lift    coefficient    obtained 

permits  of  a  considerable  reduction  in  the  landing 
speed. 

2.  That    by   adjusting    the    flap    to    correspond    with    the 

minimum  drag  for  the  particular  angle  of  incidence 
at  which  the  machine  travels  over  the  ground,  the 
distance  necessary  to  take  off  may  be  reduced  by  13%. 

3.  The  distance  required  to  pull  up  after  having  landed  can 

be  diminished  by  setting  the  flaps  at  a  large  angle  of 
pitch. 

4.  The  maximum  flying  speed  can  be  increased  by  giving  to 

the  flaps  a  small  negative  angle  at  the  corresponding 
angle  of  flight  for  maximum  speed. 

5.  A  slight  gain  in  climbing  speed  can  be  obtained  by  the 

use  of  flaps. 

The  mechanical  dfficulties  involved  in  securing  a  hinged 
wing  section  are  considerable,  but  it  is  apparent  from  these 
experiments  that  a  considerable  gain  would  accrue  in  aero- 
dynamical efficiency. 

Balance  of  the  Control  Surfaces. — When  referring  to  the 
elevator  it  was  stated  that,  in  order  to  reduce  the  strain  upon 
the  pilot  when  working  the  controls,  the  method  of  balancing 
the  control  surface  was  desirable.  Similar  considerations  make 
it  advisable  to  balance  both  the  rudder  and  the  ailerons  upon 
large  machines — i.e.,  machines  of  greater  weight  than  5000  Ibs. 
This  may  be  effected  in  two  ways  (see  Fig.  272)  : 

(i.)    By  adding  an  extension  which  projects  in  front  of  the 

main  portion  of  the  surface, 
(ii.)  By  placing  the  hinge  about  which  the  control  rotates 

some  distance  behind  the  leading  edge. 

In  both  these  methods  the  air  forces  upon  the  surface  in 
front  of  the  hinge  produce  about  the  hinge  a  moment  of 
opposite  sign  to  that  of  the  main  control  surface,  and  therefore 
reduce  the  effort  required  to  move  it  by  twice  this  amount.  The 
first  method  has  been  most  frequently  employed  in  practice  in 
this  country,  but  the  second  method  possesses  many  more 
advantages,  and  has  been  used  on  the  latest  Handley-Page 


AEROPLANE    DESIGN 


machine  (V-I5OO).  In  order  to  decide  upon  the  area  of  the 
extension  required,  it  is  necessary  to  determine  the  moment  of 
the  main  surface  about  the  hinge  for  various  angles  of  deflection 
and  then  to  select  an  extension  which  will  produce  the  necessary 
degree  of  balance  over  this  range  of  angles.  For  most  accurate 
results  a  model  of  the  wing  and  flap  with  extension  should  be 
made  and  tested  in  the  wind  tunnel,  the  size  of  the  extension 
being  altered  until  satisfactory. 

If  such  a  procedure  is  not  possible,  the  size  of  the  extension 
must  be  deduced    from  whatever   results   are   available.      The 


Angle 


FIG.  271. — Moments  about  Hinge  of  Wing  Flap. 


following  example  indicates  a  rough  method  of  arriving  at  the 
necessary  dimensions  of  an  extension  to  a  wing  flap  for  balancing 
purposes.  Fig.  271  gives  the  moments  about  the  hinge  for  the 
wing  flap  described  on  page  374.  The  increase  of  moment  per 
degree  of  deflection  of  flap  at  o°  pitch  of  wing  =  '0004  ft.  Ibs. 
The  section  of  the  extension  used  will  be  that  of  the  Tail  Plane 
No.  3,  whose  dKy/d8  —  "033,  and  the  average  position  of  whose 
C.P.  will  be  taken  at  0*23  chord  from  the  leading  edge. 

Then  for  balance  the  moment  of  the  extension  about  the 
hinge  must  equal  '0004  ft.  Ibs.  per  degree — that  is,  the  load  on 
the  extension  x  2  x  c  =  '0004  ft.  Ibs. 


DESIGN    OF   THE   CONTROL   SURFACES  377 

The  C.P.  coefficient  is  -23  ;  therefore  the  distance  from  hinge  at 
which  the  resultant  force  upon  the  extension  may  be  assumed 
to  act  is 

=  (i  -  -23)  a  -  1-155" 

=  77  a  -  0*0963  feet 
whence      2  x  -033  x  '00237   x  40*  x  a  x  £(7 7  a  -  0*0963)  =  '0004 

Taking  an  approximate  value  for  b  of  1-5,  we  have 

0-3130(770  -  °'°963)  =  *00°4 
or  77  a2  -  0*0963  a  =  0*00128 

Solving  this  quadratic 

a  =  '206  feet  =  2*47" 

so  that  the  dimensions  of  extension  necessary  to  balance  the 
flap  upon  the  assumptions  made  =  1.5"  x  2*47".  In  practice 


111 

m 

i 

A 

1 

1 

i  ^ 

FIG.  272. — Balanced  Ailerons. 

the  dimensions  1-5"  x  2'$"  would  be  adopted.  Such  an  exten- 
sion increased  to  the  same  scale  as  the  wing  and  flap  would  give 
the  required  balance  upon  a  full-size  machine. 

The  above  calculation  is  given  to  indicate  the  method  to  be 
used  for  calculating  the  size  of  a  balancing  extension. 

It  is  obvious  that  the  assumptions  made  cannot  be  strictly 
justified,  since  the  position  of  the  C.P.  of  the  extension  varies 
with  the  angle  of  incidence.  Moreover,  end-effect  will  be 
important  at  the  wing-tips.  Nevertheless,  such  a  calculation 
is  extremely  useful  in  the  initial  stages  of  a  new  design  as 
affording  an  indication  of  the  probable  size  required.  This  can 
be  altered  subsequently,  if  experience  shows  it  to  be  necessary 
after  a  trial  flight  has  been  made. 

For  securing  balance  by  the  second  method,  recourse  must 
also  be  made  to  wind-channel  experiments.  An  examination 
of  the  pressure-distribution  diagrams  over  the  rear  portion  of  a 
wing  section  will  be  of  much  assistance  in  this  direction.  In 


378  AEROPLANE    DESIGN 

general  the  shape  is  found  to  be  approximately  triangular,  as 
will  be  seen  by  reference  to  Fig.  48.  For  a  triangle  the  C.P.  will 
be  at  one-third  the  altitude  from  the  base  line,  hence  it  can  be 
inferred  that  the  position  of  the  hinge  for  full  balance  in  this 
method  should  be  at  one-third  the  chord  of  flap  from  its  leading 
edge.  In  order  to  avoid  the  possibility  of  the  flap  being  over- 
balanced, and  hence  tending  to  increase  its  deflection  relative  to 
the  remainder  of  the  section,  it  would  be  advisable  to  place  the 
hinge  at  about  0*3  times  the  flap  chord  from  the  leading  edge. 

These  methods  of  balancing  are  applicable  to  each  of  the 
control  surfaces. 

Construction  of  Control  Surfaces. — The  controlling  sur- 
faces are  built  up  much  as  portions  of  wings.  A  strong  leading 
edge  serves  to  take  the  hinges,  and  forms  as  it  were  a  '  back- 


FIG.  273. — Dual  Control  System. 

bone '  from  which  may  radiate  ribs  of  light  construction  to  the 
trailing  edge.  The~  trailing  edge,  in  the  case  of  the  wing-flaps, 
will  be  similar  to  the  rigid  part  of  the  wings.  In  the  case  of 
the  elevators,  and  more  especially  in  the  case  of  the  rudder,  thin 
tubing  of  about  10  mm.  diameter  will  be  found  useful.  Short 
levers  of  streamlined  section  are  fixed  to  the  backbone  or  spars, 
and  connected  by  wires  to  the  control  lever  in  the  pilot's 
cockpit.  The  wires,  or  rather  thin  cables,  may  be  guided  round 
corners  by  pulleys  or  bent  copper  tubing.  They  should  be 
covered  as  much  as  possible,  so  as  to  diminish  head  resistance, 
and  should  therefore  be  placed  inside  the  wings,  inspection 
doors  being  provided  where  necessary  in  the  wings  ;  and  for  the 


DESIGN    OF   THE   CONTROL   SURFACES  379 


TAI LPLANE1   &  ELEVATORS 


FIN 


FIG.  274. — Tail  Unit  Components.     (See  also  p.  412.) 


IS  Cacfc* 


Cockpit- 


FIG.  275.  —  Variable  Incidence  Gear  for  Tail  Plane. 


380  AEROPLANE    DESIGN 

tail  unit  should  enter  the  fuselage  as  soon  as  convenient.  The 
success  with  which  the  designer  balances  his  controlling  surfaces 
is  shown  by  the  consequent  lightening  of  the  control  lever,  and 
more  especially  is  this  the  case  with  large  machines. 

The  design  of  the  control  is  a  simple  matter  when  the  loads 
spread  over  the  control  surfaces  have  been  assessed  for  the 
highest  speeds  and  the  greatest  angles,  and  their  moments 
about  their  hinges  obtained  by  locating  the  c.p.  The  pulls  in 
the  connecting  wires  follow  at  once,  and  the  problem  of  the 


Reproduced  by  courtesy  of  ' Flight.'' 

FIG.  276. — Double  Tail  Unit  for  Large  Machine. 

control  lever  reduces  to  the  question  of  a  short  cantilever  pro- 
jecting vertically  from  a  horizontal  pivot  tube.  If  the  elevators 
are  attached  to  levers  at  the  ends  of  this  tube — that  is,  near  the 
sides  of  the  fuselage — the  tube  must  be  designed  for  combined 
torsion  and  bending. 

The  fuselage  should  be  strengthened  where  it  takes  the 
strain  of  the  control  lever  and  rudder  bar.  The  rudder  bar, 
arranged  for  the  feet,  may  be  conveniently  made  of  wood  with 
metal  fittings.  The  vertical  pivot  should  be  made  adjustable 
along  the  fuselage,  with  lengthened  strips  for  the  rudder  cables, 
so  as  to  be  available,  without  any  inconvenience,  for  pilots  of 
different  sizes. 


CHAPTER  XII. 
PERFORMANCE. 

Definition. — The  factors  upon  which  the  performance  of  a 
machine  depends — that  is,  the  maximum  speed  which  it  is  able 
to  attain  at  varying  altitudes  and  the  time  it  takes  to  reach  such 
altitudes — were  considered  at  some  length  in  Chapter  I.,  and 
those  pages  should  be  again  consulted  at  this  stage.  In  this 
chapter  the  relation  between  these  various  factors  will  be  investi- 
gated in  their  effect  upon  the  increase  or  decrease  of  the 
efficiency  of  the  aeroplane,  and  some  practical  methods  of 
actually  determining  the  performance  of  machines  in  flight  will 
be  given. 

The  primary  object  of  the  aeroplane  is  to  transport  a  certain 
useful  load  from  one  point  to  another,  using  the  air  as  a  medium 
of  travel.  It  must  therefore  be  provided  with  a  surface  capable 
of  developing  the  necessary  reaction  to  overcome  the  force  of 
gravity,  while  offering  at  the  same  time  a  minimum  resistance 
to  forward  motion  through  the  air.  The  development  of  the 
modern  wing  section,  as  outlined  in  Chapter  III.,  had  for  its 
aim  the  accomplishment  of  this  purpose.  The  area  of  the  sup- 
porting surfaces — that  is,  the  wings — must  obviously  be  such 
that  the  -reaction  upon  them  is  equal  to  the  weight  of  the 
machine.  This  reaction,  as  we  have  already  seen,  is  termed 
the  lift  of  the  wings.  Such  lift  is  always  accompanied  by  a 
resistance  or  drag  at  right  angles  to  it.  The  drag  of  the 
complete  machine  is  made  up  of  two  parts — namely,  the  wing 
resistance  and  the  body  resistance.  It  is  the  aim  of  the  designer 
to  obtain  a  wing  section  in  which  the  ratio  of  L/D  is  a 
maximum  for  the  speed  at  which  he  proposes  the  machine 
under  consideration  should  fly. 

The  efficiency  of  the  wing  surfaces  is  largely  influenced  by 
'  end  effect,'  and  in  order  to  obtain  a  highly  efficient  wing  the 
aspect  ratio  must  be  high.  Increase  of  aspect  ratio  leads  to  a 
corresponding  increase  in  the  weight  and  constructional  diffi- 
culties, so  that  apparently  a  definite  limit  for  greatest  efficiency  is 
soon  reached.  The  maximum  aspect  ratio  adopted  to-day  is  in 
the  neighbourhood  of  10. 

All  resistances  other  than    that  of  the  wings   are  grouped 


382  AEROPLANE    DESIGN 

together  under  the  term  '  body  resistance.'  This  resistance 
varies  approximately  as  the  square  of  the  speed,  but  a  factor 
which  leads  to  considerable  uncertainty  in  this  direction  is  the 
slip  stream  from  the  airscrew.  In  the  case  of  the  tractor 
machine  the  body  moves  directly  in  this  slip  stream,  and  its 
resistance  is  thereby  increased  relative  to  the  remainder  of  the 
machine.  Moreover,  interference  between  the  various  com- 
ponents leads  to  a  further  modification,  which  it  is  very  difficult 
to  estimate.  The  body  resistance  becomes  of  increasing  relative 
importance  as  the  speed  of  flight  becomes  greater  and  greater. 
Examination  of  the  resistance  curves  for  the  wings  shown  in 
Fig.  278  indicates  that  the  wing  resistance  remains  fairly 
constant  over  a  considerable  range  of  speeds,  whereas  the 
body  resistance  increases  as  the  square  of  the  speed.  The 
minimum  total  resistance  will  occur  when  the  wing  and 
body  resistance  are  approximately  equal  in  amount,  and  the 
speed  corresponding  to  this  will  be  the  most  economical  for  flight. 

Turning  next  to  a  consideration  of  the  Engine  power,  the 
first  point  to  be  observed  is  that  the  thrust  exerted  by  the  engine 
must  be  sufficient  to  propel  the  wing  surfaces  through  the  air  at 
such  a  speed  that  their  reaction  overcomes  the  weight  of  the 
machine.  The  forces  tending  to  prevent  the  attainment  of  such 
speed  are  the  wing  and  body  resistances  referred  to  above,  hence 
for  horizontal  flight  at  a  particular  speed  it  is  necessary  that  the 
engine  thrust  must  be  at  least  equal  to  the  drag  of  the  machine. 
An  estimate  of  the  horse-power  required  necessitates,  therefore, 
a  knowledge  of  the  resistance  to  be  overcome  at  the  various 
speeds  of  flight.  It  is  also  essential  that  a  reserve  of  power  is 
available  in  order  that  the-  machine  may  climb.  The  excess  of 
power  supplied  over  that  required  for  horizontal  flight  is  the 
horse-power  available  for  climbing,  and  this  being  known  a 
simple  calculation  will  enable  the  rate  of  climb  to  be  determined. 
The  maximum  rate  of  climb  will  correspond  with  that  speed  at 
which  the  excess  power  is  greatest. 

The  prediction  of  performance  necessitates  a  knowledge  of 
the  resistance  of  the  machine  at  various  flight  speeds,  together 
with  the  excess  horse-power  available  at  that  speed.  The 
following  paragraphs  show  one  method  of  determining  these 
quantities  for  a  machine  of  new  design. 

The  Resistance  of  the  Machine. — (a)  Wing  Resistance. — 
The  wing  resistance  is  deduced  directly  from  the  aerodynamic 
characteristics  of  the  section  employed.  It  is  first  necessary  to 
determine  the  lift  coefficient  corresponding  to  various  speeds  of 
flight.  For  this  purpose  the  fundamental  equation  (Formula 


PERFORMANCE  383 

13)  is  used.  This  gives  Ky  for  varying  values  of  V.  From 
the  wing-section  characteristics  the  value  of  the  drag  coefficient 
corresponding  to  each  Ky  is  obtained,  which  gives  the  corre- 
sponding flight  speed.  The  drag  coefficient  and  the  speed  of 
flight  being  known,  the  wing  resistance  follows  from  the  funda- 
mental equation  (Formula  14).  These  values  should  be  plotted 
on  a  speed  base. 

(b)  Body  Resistance. — The  estimation  of  the  body  resistance 
is  a  matter  of  some  difficulty,  and  recourse  must  be  had  to  wind- 
tunnel  data  wherever  available.  It  is  advisable  to  make  a  point 
of  collecting  resistance  data  whenever  an  opportunity  occurs, 
particularly  the  resistances  of  a  complete  machine,  such  as  that, 
for  example,  given  in  Chapter  VI.  for  the  B.E.  biplane.  The 
figures  given  in  Chapter  I.  will  also  be  useful  in  this  connection, 
and  will  serve  as  a  base  upon  which  to  make  comparisons. 
The  accuracy  of  the  entire  performance  calculation  is  directly 
dependent  upon  this  estimate  of  body  resistance,  and  hence  it  is 
essential  that  it  should  be  carried  out  as  carefully  as  possible, 
due  allowance  being  made  for  those  parts  in  the  airscrew  slip 
stream. 

If  the  machine  has  already  been  built,  it  is  possible  to  deter- 
mine the  body  resistance  by  noting  the  gliding  angle.  If  this 
be  9  we  then  have  the  relationship  tan  9  =  D/L  where  D 
represents  the  total  drag  of  the  machine,  and  L  the  lift  of 
the  wings.  From  the  total  drag  the  resistance  of  the  wings 
is  subtracted,  and  the  remainder  will  be  the  body  resistance. 
This  is  in  most  cases  the  more  accurate  method,  it  being  usually 
found  that  the  estimated  '  body  resistance '  is  higher  than  the 
observed  body  resistance.  The  body  resistance  (R)  being  known 
for  any  speed  v,  then  at  any  other  speed  (V)  the  resistance  is 
obtained  from  the  equation 

R    V'' 
Resistance  at  speed  V  =  —  -!-— 

v* 

Add  the  body  resistance  at  any  speed  to  that  of  the  wings 
for  the  same  speed,  and  the  total  resistance  of  the  machine  for 
that  speed  is  obtained.  A  curve  of  total  resistance  against 
speed  can  then  be  drawn. 

In  determining  the  wing  resistance  of  a  machine,  allowance 
must  be  made  for  the  following  factors  : 

1.  Effect  of  slip  stream  of  airscrew. 

2.  Interference  effects. 

3.  The  stagger  and  aspect  ratio  of  the  wings. 


384  AEROPLANE    DESIGN 

Horse-power  required.  —  (a)  To  overcome  wing  resistance  : 

H.P  required  =  Resistance  x  Velocity 

55o 
-  Kx(P/*-)AV*  x  V/550 


550 

Knowing   Kx  corresponding  to  each   flight  speed  V,  the  wing 
H.P.  can  be  calculated. 

(If)  To  overcome  body  resistance  :  similarly, 

H.P.  required  =?^.— 
v*  55° 
RV3 


From  this  equation  the  '  body '  H.P.  can  be  determined  for 
several  values  of  V.  It  will  be  found  most  convenient  in  calcu- 
lating the  total  horse-power  required  to  use  the  tabular  method 
•of  setting  out  the  work. 

Horse-power  available.  —  As  stated  in  Chapter  I.,  this 
•depends  both  upon  the  engine  and  the  airscrew.  The  efficiency 
of  each  of  these  units  depends  largely  upon  the  conditions 
under  which  it  is  working,  and  data  respecting  the  variation  of 
•engine-power,  with  altitude  and  revolutions  per  minute,  should 
be  obtained  from  tests  carried  out  independently  or  by  the 
manufacturer.  It  is  found  that  the  brake  horse-power  of  an 
•engine  varies  almost  directly  as  the  density  of  the  air,  and  is 
practically  independent  of  its  temperature. 

The  efficiency  of  the  airscrew  varies  with  its  forward  speed, 
and  may  be  calculated  with  a  considerable  degree  of  accuracy  in 
the  manner  set  forth  in  Chapter  IX.  The  horse-power  required 
to  drive  the  airscrew  at  various  speeds  can  be  determined  from 
its  torque  curve.  If  Q  be  this  torque,  then  the  horse-power 
required  to  drive  the  airscrew  at  n  revolutions  per  second 

_  2  TT  n  Q 

55° 

This  horse-power  should  then  be  plotted  on  the  base  of  '  n '  and . 
superposed  on  the  B.H.P.  curve  of  the  engine  similarly  plotted 
on   a  base  of  '  n.'     The  intersection  of  these  curves  gives  the 
maximum  horse-power  available  at  that  translational  speed  of 
the  airscrew.     The  efficiency  of  the  airscrew  being  known,  it  is 


PERFORMANCE  385 

then  an  easy  matter  to  determine  the  maximum  available  horse- 
power to  drive  the  machine. 

On  plotting  (i)  total  H.P.  required  to  overcome  resistance 
of  machine  at  ground  level ;  (2)  power  available  at  ground  level, 
on  a  speed  base,  it  can  be  seen  from  the  curve  what  power  is 
available  for  climbing,  and  also  the  fastest  climbing  speed. 

Similarly,  by  calculating  the  above  quantity  for  the  density 
corresponding  to  the  maximum  height  it  is  desired  to  fly  at,  it 
will  be  seen  what  is  the  highest  speed  attainable  at  this  height. 

Rate  of  Climb. — The  difference  between  the  ordinates  of 
the  H.P.  required  and  the  H.P.  available  curves  shows  the  H.P. 
available  for  climbing  at  each  speed.  The  maximum  difference 
will  give  the  maximum  rate  of  climb  to  be  expected,  which  can 
be  calculated  thus  : — 

Let  P  represent  the  horse-power  available  for  climbing. 
Then  rate  of  climb  in  feet  per  minute 

=  r  =  P  x  33ooo/weight  of  machine 

The  points  at  which  the  H.P.  curves  intersect  determine  the 
maximum  and  minimum  flying  speeds  respectively,  and  thus 
a  calculated  estimate  of  the  performance  of  the  machine  is 
obtained.  The  nearness  with  which  these  results  approach 
those  experimentally  obtained  will  be  a  measure  of  the  accuracy 
of  the  estimated  resistances  and  other  assumptions. 

Performance  Calculations.— An  example  of  the  method 
of  predicting  the  performance  of  an  aeroplane,  such  as  should 
be  carried  out  when  designing  a  new  type  of  machine,  will  now 
be  given.  For  this  purpose  the  particulars  of  the  machine 
referred  to  in  Chapter  V.  will  be  used.  It  is  required  to  deter- 
mine the  maximum  speed  and  rate  of  climb  of  this  machine  at 
ground  level  when  fitted  with  a  150  H.P.  engine  and  an  airscrew 
possessing  an  efficiency  of  80%.  The  estimated  resistance  of 
the  machine  less  wings — that  is,  its  body  resistance — is  equal  to 
I5olbs.  at  100  feet  per  second.  The  characteristics  of  the  wing 
.section  are  as  follows  : — 

CHARACTERISTICS  OF  THE  WING  SECTION. 

0  o°  2°          4°  6°          8°          10°         12°         14° 

Ky     ...     '097       -192       -273       -347       -421       -492       '555       '59 
Kx     ...     '0167     '0165     '0199     '0261     '0355     '0452     '0551     '0742 

c  c 


386  AEROPLANE    DESIGN 

From  these  characteristics  the  wing  resistance  at  varying  speeds 
is  calculated  in  the  following  manner.     From  formula 

w 


0     ,        .         . 

Substituting 


f>  A'K 


2000  2-100 

—-  -  -  —   =  -2— 

•00237        X       366       X        Ky  Ky 


Notice  that  the  effective  supporting  wing  area — A' — is  used  in 
this  formula.  From  this  relationship  the  velocity  of  flight 
corresponding  to  varying  values  of  Ky,  and  consequently  of  the 
angle  of  incidence,  can  be  calculated,  whence  the  determination 
of  the  wing  resistance  is  obtained  by  using  the  formula 

Rw  =  Kx  P  A  V2 

<r 

where  Rw  represents  the  wing  resistance  and  A  the  total  area  of 
the  wing  surface  =  414  square  feet.  Tabulating  the  results  we 
obtain 

TABLE  LVI. 

8                            o°  i°  2°  4°           6° 

V2          ...  ...     23700  15800  11980  8430  6630 

V  (f.p.s.)  ...          154  126  109*2  91*8  81*4 

-?AV2    ...  ...     23250  15400  11750  8260  6500 

RW                                 388  253  194  164         170 

0  8°  10°  12°         14° 

V2     ...    ...   5460    4670    4150   3900 

V  (f.p.s.)     ...    73'9    68'4    64-4    62-5 

^AV2    ...         ...       5350        4580        4070       3820 

& 

Rw          19°  207  224         284 

Body  Resistance. — The  resistance  of  the  rest  of  the  machine 
is  proportional  to  the  square  of  the  speed  of  the  machine,  con- 
sequently the  resistance  can  be  obtained  from  the  formula 


The  figure  used  for  the  body  resistance  of  the  machine,  which  in 
this  case  has  been  assessed  at  I5olbs.  at  100  f.p.s.,  should  be 
most  carefully  estimated  from  all  available  data,  the  resistance 


PERFORMANCE 


387 


of  each  member  and  detail  being  checked  wherever  possible  by 
reference  to  full-scale  results.  The  accuracy  of  the  predicted 
performance  depends  to  a  large  extent  upon  this  estimate. 
Tabulating  the  results  for  the  body  resistance  we  have 


V2 
RB 


23700 
•      356 


15800 
237 


11980 
180 


8430 
126 


6630 

100 


5460 
82 


4670 
70 


415° 
62 


3900 

49 


Adding  together  Rw  and  RB  the  total  resistance  of  the  machine 
for  varying  flying  speeds  is  obtained,  namely, 

Rw  +  RB     ...      744     490     374     290     270     272     277     286     333 


V,r 


FIG.  277. — Power  Factors  from  Typical  Engine  and  Airscrew  Curves. 


Horse-power  required. — Having  obtained  the  total  resistance, 
the  horse-power  required  is  obtained  by  multiplying  by  V/55O. 
The  results  are  tabulated  below : — 


V/550       ...     '288     "229     "199     "167     '148     "134 
H.P.         ...      208      112      74-5     48-5       40      36-5 


•124     '117     '114 
34*4     33*5     38 


Horse-power  available. — It  will  be  assumed  that  the  engine 
and  airscrew  are  designed  to  give  the  maximum  efficiency  at  a 
forward  speed  of  100  m.p.h.,  and  that  the  variation  in  power  at 
other  speeds  follows  a  curve  similar  to  that  shown  in  Fig.  277. 


388 


AEROPLANE    DESIGN 


V  (m.p.h.) 
V  (f.p.s) 


Fp  from  curve 
H.P.  available 


100 
146-8 

I'O 
I"0 
120 


TABLE  LVII. 

90 
132 

*9 

•98 

118 


80 

70 

60 

5° 

40 

117-2 

102-8 

88 

73*4 

587 

•8 

7 

•6 

'5 

'4 

'94 

•88 

•80 

•70 

•56 

H5 

106 

96 

84 

67 

In  the  above  table  the  horse-power  available  is  obtained  by 
multiplying  Fp  by  the  horse-power  of  the  engine  (150)  and  by 
the  maximum  efficiency  of  the  airscrew  (0*8).  The  curves  of 


90  100 

Vcloofy  (I 


FIG.   278. — Performance  Curves. 

horse-power  required  and  horse-power  available  must  now  be 
plotted  on  a  speed  base,  as  shown  in  Fig.  278.  The  intersection 
of  the  curves  shows  the  maximum  speed  which  the  machine  is 
capable  of  attaining — namely,  128  f.p.s.  or  87  m.p.h.  The 
maximum  horse-power  available  for  climb  is  52  at  a  forward 
speed  of  85  f.p.s.,  whence  the  maximum  rate  of  climb 

-  =  860  feet  per  minute. 


2000 


A  further  practical  example  of  the  calculation  of  the  per- 
formance of  a  machine  is  given  in  Chapter  XIII. 


PERFORMANCE  389 

Measurement  of  Performance. — Having  dealt  with  the 
method  of  predicting  performance  for  a  machine  of  new  design, 
it  is  desirable  to  consider  various  experimental  methods  whereby 
the  actual  performance  of  such  a  machine  when  built  can  be 
checked.  The  chief  difficulty  met  with  in  making  these  measure- 
ments is  due  to  variation  in  the  medium  in  which  flight  occurs. 
As  is  generally  known,  the  pressure,  and  consequently  the 
density  of  the  atmosphere,  diminishes  with  increasing  altitude. 
Further,  as  has  already  been  shown  in  Fig.  7,  there  is  also  a 
fall  in  the  temperature.  The  instruments  for  the  measurement 
of  performance  are  directly  dependent  upon  the  condition  of  the 
air,  and  it  is  this  fact  which  renders  the  accurate  measurement 
of  the  performance  of  a  machine  a  difficult  operation.  In 
addition  to  the  above  variations,  it  must  also  be  borne  in  mind 
that  the  temperature  may  vary  very  considerably  at  the  same 
altitudes,  owing  to  up  and  down  air  currents,  to  seasonal  changes, 
and  to  change  of  latitude.  Much  of  our  knowledge  of  this 
subject  is  due  to  Mr.  W.  H.  Dines,  F.R.S.,  who  has  carried  out 
and  controlled  observations  for  several  years.  Table  LVIII.  is 
a  summarised  result  of  his  labours. 


TABLE  LVIII. — MEAN  ATMOSPHERIC  PRESSURE,  TEMPERATURE, 
AND  DENSITY  AT  VARIOUS  HEIGHTS  ABOVE  SEA  LEVEL. 

Height  in  F  Mean  pressure      Mean  temp.         Mean  density 

kilometres.  millibars.  C°  abs.          kgm/cu.  metre. 

0  ...  O         ...         1014         ...         282         ...         1*253 

1  ...  3280  ...  900  ...  278  ...  1-128 

2  ...  6560  ...  795  ...  273  ...  1-014 

3  ...  9840  ...  699  ...  268  ...  0*909 

4  ...  13120  ...  615  ...  262  ...  0*818 

5  ...  16400  ...  568  ...  255  ...  0735 

6  ...  19680  ...  469  ...  248  ...  0^658 

7  ...  22960  ...  407  ...  241  ...  0*589 

It  is  convenient  to  choose  some  density  as  a  standard  and  to 
call  it  unity,  and  then  to  refer  all  other  densities  to  this  standard 
by  expressing  them  as  percentages  of  this  standard  density. 
The  standard  taken  by  the  R.A.E.  is  the  density  of  dry  air  at 
a  pressure  of  760  mm.  and  at  a  temperature  of  16°  C.,  where  the 
density  is  1*221  kgm.  per  cubic  m.  In  order  therefore  to  obtain 
a  strict  basis  of  comparison,  all  observed  aeroplane  performances 
must  be  reduced  to  this  standard. 


39° 


AEROPLANE    DESIGN 


TABLE  LIX. — PERCENTAGE  OF  STANDARD  DENSITY  DUE  TO 
CHANGE  OF  ALTITUDE, 


Height. 


1000 

2OOO 

3000 

4000 
5000 
6000 
7000 
8000 
9000 

1 0000 


Percentage  of 
standard  density. 

102*6 

99'4 
96'3 

90*3 
87-4 
84*6 
81-9 
79-2 

76-5 
74-0 


Height. 

1 1  ooo 
12000 
13000 
14000 
15000 
16000 
17000 
18000 
19000 

20000 


Percentage  of 
standard  density. 

717 
69'5 


63*0 
6i'o 
59'i 
57'i 
55'2 
53  "3 


The  Airspeed  Indicator  (Anemometer). — The  measure- 
ment of  the  speed  of  a  machine  is  the  first  essential  of  a 
performance  test.  This  may  be  made  either  by  direct  measure- 
ment of  the  time  taken  to  cover  a  measured  distance  or  by 
using  a  speed  indicator,  which  must,  however,  have  been  cali- 
brated by  the  direct  test.  The  method  of  carrying  out  the 
direct  test  will  be  considered  subsequently. 

Briefly  summarised,  the  requirements  and  conditions  of 
aeronautical  airspeed  indicators  are  as  follows: 

1.  Weight  and  Head  Resistance. — Must  both  be  small. 

2.  Mechanical  Strength.-^-T\\e  severe  conditions  of  vibration 
preclude   the   possibility   of  using   instruments  which    are   not 
mechanically  strong,  or  which  cannot  be  made  so  without  the 
addition  of  undue  weight.     Both  the  head  proper,  and  the  trans- 
mitting and  indicating  parts,  must  be  simple,  light,  strong,  and 
free  from  the  need  of  delicate  adjustment  or  frequent  testing. 

3.  Position. — The  head  must,  so  far  as  practicable,  be  out  of 
reach    of  irregular   currents  or  eddies,   and   therefore  at  some 
distance  from  the  indicator,  which  of  course  must  be  placed  in 
the   pilot's    cockpit.      The    best   position    would    appear-  to   be 
towards  the  end  of  a  wing-tip  if  the  transmission  gear  can  be 
made  satisfactory. 

4.  Influence  of  Gravity. — On  account  of  the  very  considerable 
angles  of  heeling  and  pitching  which  occur  in  flight,  any  instru- 
ment which  depends  for  its  action   upon  weights  or   a   liquid 
manometer  is  useless.     Any  required  forces  must  be  applied  by 
means  of  springs,  or  if  pressures  are  to  be  registered  it  must  be 


PERFORMANCE  391 

by  means  of  spring  gauges.  Further,  all  parts  of  the  instru- 
ment must  be  so  balanced  that  in  any  position  the  readings  are 
independent  of  the  effect  of  gravity. 

The  ordinary  form  of  speed  indicator  is  the  Pitot  Tube, 
which  is  an  instrument  measuring  the  pressure  difference 
between  a  current  of  moving  air  and  the  corresponding  stationary 
air.  It  consists  essentially  of  two  tubes,  namely,  the  dynamic 
tube,  the  end  of  which  is  open  to  and  faces  the  moving  air 
stream  ;  and  the  static  tube,  which  carries  a  ring  of  concentric 
holes  over  which  the  air  stream  flows.  The  underlying  theory 
of  the  Pitot  tube  is  fairly  simple. 

Let  V  =  velocity  of  the  air  stream 

w  —  weight  of  i  cubic  foot  of  air 
/  =  static  or  barometric  pressure 
h  =  potential  pressure  head 

Then  by  Bernouilli's  theorem  : 

•  //  +  —  +  -  —  -  =  constant 

W  2  g 

Now  for  horizontal  motion  the  potential  pressure  head  h 
remains  constant  ;  hence  we  may  write 

i>       (VV2 

£  +  v  —  L  =  constant 

W  2g 

Let  P  be  the  so-called  dynamic  pressure  transmitted  by  the 
inner  tube.  At  the  mouth  of  this  tube  the  velocity  is  reduced 
to  zero,  hence 


W  W  2  g 

Or  P  -/  =  (V)2 

W  2g 

The  quantity  (P  —  p)jw  is  the  difference  in  pressure  measured 
by  the  manometer.  Denoting  this  by  H,  the  above  expression 
may  be  written 

(V)2  =  2£-H 

In  order  to  allow  for  errors  in  construction,  the  law  of  the 
Pitot  tube  is  generally  written 

(V)2  =  K  .  2  ^  H  ............  Formula  99 

where  K  is  a  correction  factor  to  be  determined  by  calibration 
of  the  actual  tube.     It  is  generally  equal  to  unity, 


392 


AEROPLANE    DESIGN 


The  advantages  of  the  Pitot  tube  over  other  instruments 
are  : 

1.  Absence  of  any  kind  of  friction,  as  there  is  practically  no 

displacement  of  air  along  the  the  tube. 

2.  Comparative  ease  of  reproducing  exactly  similar  tubes, 

thus  obviating  the  necessity  of  individual  calibration. 

3.  Very  small  wind  resistance. 

If  the  potential  pressure  head  in  Formula  99  is  read  on  a 
gauge  containing  a  liquid  of  density  '  dl  while  the  density  of  the 
air  current  is  p,  the  above  equation  takes  the  form 


V2  =  K.2<fH- 
P 


Diaphragm 


Dynamic^ 


Pressure 


Stable 


Needle 


Ppcssure 


Dial 


Pressure  Tube 
5  StehcTube 


FIG.  279. — Airspeed  Indicator. 


Dynamic 
Pressure 

FIG.  280.— Pitot  Tube. 


Recent  investigations  have  shown  that  almost  any  form  of 
dynamic  opening  is  satisfactory,  but  that  the  static- opening 
must  be  specially  designed  in  order  that  the  coefficient  K  may 
be  equal  to  unity. 

When  used  on  an  aeroplane,  tbe  Pitot  tube  is  generally  fitted 
to  the  leading  edge  of  the  top  wing  and  to  one  side  of  the  centre 
line  of  the  machine,  so  as  to  be  out  of  the  slip  stream  of  the 
airscrew.  The  speed-indicator  dial  is  fixed  in  the  pilot's 
cockpit,  the  general  arrangement  being  shown  in  Fig.  279.  The 
dynamic  pressure  of  the  air  is  transmitted  to  a  small  airtight 
cylinder  divided  into  two  parts  by  a  rubber  diaphragm,  the 
space  on  the  opposite  side  of  the  diaphragm  being  connected  to 


PERFORMANCE 


393 


the  static  tube.  The  movement  of  this  diaphragm  under  the 
action  of  the  air  forces  is  communicated  to  a  needle  which 
registers  the  air  speed.  These  instruments  are  carefully  cali- 
brated by  means  of  the  ordinary  type  of  Pitot  tube,  shown  in 
Fig.  280. 

Another  form  of  airspeed  indicator  depends  upon  the 
principle  of  the  Venturi  meter,  familiar  to  students  of  hydraulics. 
The  Venturi  tube  consists  of  a  short  converging  inlet  followed 


FIG.  281. — Venturi  Airspeed  Indicator. 

by  a  long  diverging  cbne,  the  entrance  and  exit  diameters  being 
usually  made  equal,  so  that  the  instrument  may  be  inserted  as 
part  of  a  pipe  line.  (See  Fig.  281.)  As  shown,  there  is 
generally  a  short  cylindrical  throat,  and  the  converging  part  has 
somewhat  the  shape  of  a  '  vena  contracta,'  but  its  exact  form  is 
not  important.  The  exit  cone  has  a  total  angle  of  about  5°, 
this  angle  having  been  found  to  give  the  minimum  frictional  loss 
for  a  given  increase  of  diameter.  When  a  current  of  fluid  passes 


FIG.  282. — Venturi  Tube. 

through  the  tube  the  pressure  in  the  throat  is  less  than  at  the 
entrance  to  the  converging  inlet  by  an  amount  that  depends 
upon  the  ratio  between  the  entrance  area  and  the  throat  area, 
the  density  of  the  fluid,  and  the  speed  of  flow.  If  the  tube  is 
provided  with  side  holes  and  connections  to  a  differential  gauge 
by  which  this  pressure  difference  may  be  observed,  it  constitutes 
a  Venturi  meter.  The  ratio  between  the  areas  is  a  known 
constant  for  a  given  instrument,  so  that  when  the  density  of  the 
fluid  is  known  the  observed  pressure  difference  may  be  used  as  a 


394  AEROPLANE    DESIGN 

measure  of  the  speed  of  flow.  Such  an  instrument  may  be  used 
as  an  anemometer  by  pointing  it  so  that  the  wind  blows  directly 
through  it,  and  the  observed  'head'  may  then  serve  as  a  measure 
of  the  wind  speed.  This  method  has  recently  been  adopted  in 
an  aeroplane  anemometer. 

Theory  of  th  3  Venturi  Tube  (see  Fig.  282). 

Applying  the  Bernouilli  Theorem  to  a  horizontal  tube,  we 
have 

*!  +  t  =  X!  +  I 

2  g  W  2  g          W 

-    V2  P    - 


UI 

whence 
Further 

2  g                       W 

z?  -  V2  =  .2  %  H 

VA  =  va 

therefore  (  
\  a, 

or 

v           a 

x/A2  -  a2 

Formula  100. 

Now  if  A  =  a\/2,  B  will  be  equal  to  unity,  and  the  observed 
Venturi  pressure  difference  will  be  the  same  as  that  shown  by  a 
Pitot  tube. 

It  is  obvious,  however,  that  the  Venturi  pressure  difference 
can  be  made  very  much  larger  than  the  Pitot  pressure  difference 
at  the  same  entrance  speed,  and  consequently  the  gauge  reading 
with  a  Venturi  tube  anemometer  can  be  made_more  sensitive. 

At  high  speeds  the  compressibility  of  the  air  must  be  taken 
into  account  and  allowed  for  in  the  development  of  the  equation. 
Since  the  pressure  difference  may  be  made  so  much  greater  than 
with  the  Pitot  tube,  the  problem  of  making  a  satisfactory  spring 
gauge  for  indicating  the  pressure  is  much  simpler,  and  this  type 
will  probably  be  considerably  developed  in  the  near  future. 

It  will  be  observed  that  the  measurement  of  velocity  by  the 
use  of  instruments  such  as  have  just  been  described  introduces 
consideration  of  the  density  of  the  air.  This  we  have  already 
shown  varies  with  the  altitude,  hence  the  indicator  will  only  give 
correct  readings  at  one  particular  altitude  where  the  density  is 
such  as  to  agree  with  that  for  which  the  scale  on  the  instrument 
was  calibrated.  It  is  therefore  necessary  to  introduce  a  correction 
factor  in  order  to  make  allowance  for  this.  Reference  to  the 


PERFORMANCE  395 

formula  for  the  pressure  head  on  these  instruments  shows  that 
this  correction  is  proportional  to  the  density,  and  the  square  of 
the  velocity,  that  is  to  say, 

H  a  P  V2 

To  correct  the  indicator  reading  for  any  altitude  at  which  the 
density  (p)  differs  from  the  standard  it  is  necessary  to  divide  the 
reading  by  the  square  root  of  the  percentage  density  at  the 
height  in  question,  that  is 

Indicated  speed 

\l  (Percentage  density  at  altitude  considered) 

Performance  Tests  on  full-scale  Machines.  —  Having 
enumerated  the  various  factors  to  be  considered  in  making  an 
observation  of  the  velocity  of  a  machine  in  flight,  the  manner  in 
which  the  direct  test  method  is  carried  out  will  now  be  indi- 
cated. The  tests  about  to  be  described  are  those  used  at  the 
Royal  Aircraft  Establishment,  and  are  taken  from  lectures  read 
before  the  Royal  Aeronautical  Society  by  Captains  Tizard  and 
Farren.  The  simplest  test  is  that  known  as  the  ground  speed 
course,  in  which  the  aeroplane  is  flown  over  a  measured  dis- 
tance (of  1000  yards)  at  a  height  of  a  few  feet  from  the  ground. 
Observation  stations  are  placed  at  each  end  of  the  course.  At 
each  station  an  observer  is  stationed,  with  a  stop  watch  and  an 
electric  bell  switch  connected  to  a  bell  placed  in  the  other 
station.  Upon  the  leading  edge  of  the  aeroplane  passing  the 
sight  of  the  first  observer,  he  starts  his  stop  watch  and  presses 
the  bell  switch  simultaneously.  When  the  observer  at  the  other 
end  hears  his  bell  ring,  he  starts  his  watch.  The  reverse  series 
of  operations  are  carried  out  at  the, end  of  the  course,  the  second 
observer  stopping  his  watch  and  pressing  the  switch  of  the  first 
observer's  bell  as  the  leading  edge  of  the  machine  passes  his 
sight.  The  actual  time  taken  for  the  aeroplane  to  fly  over  the 
distance  between  the  stations  will  be  very  accurately  given  by 
the  mean  of  the  times  indicated  by  the  two  stop-watches.  To 
take  into  account  a  light  side  wind,  the  machine  is  allowed  to 
drift  with  the  side  wind  away  from  the  measured  line,  such 
variation  from  the  exact  distance  making  practically  no  differ- 
ence to  the  accuracy  of  the  result. 

A  second  method  is  known  as  the  altitude  speed  test. 
In  this  case  the  machine  flies  over  a  measured  distance  of 
about  4000  yards  at  an  altitude  of  approximately  3000 
feet.  The  flight  path  is  observed  by  means  of  a  reflecting 
prism  and  telescope,  the  combined  instrument  being  capable 


396 


AEROPLANE    DESIGN 


of  rotation  about  an  axis  such  that  the  aeroplane  can  be 
kept  in  view  throughout  unless  the  deviation  exceeds  800 
feet.  The  observations  are  similar  to  those  of  the  first  method. 
As  the  aeroplane  passes  across  the  telescopic  sight  of  the  first 
instrument,  the  time  is  observed  by  the  first  observer,  who 
proceeds  to  follow  the  flight  of  the  machine  by  rotation  of  his 
instrument.  When  the  machine  passes  over  the  second  station, 
the  observer  there  signals  to  the  first  station,  and  automatically 
fixes  the  position  of  the  instrument  of  the  first  observer.  The 
times  in  this  case  are  all  recorded  automatically  at  one  end  of 
the  course.  The  disadvantage  of  this  method  is  the  difficulty 
of  accurately  measuring  the  velocity  and  direction  of  the  wind. 


.P 
ti 


FIG.  283. 

This  is  approximately  achieved  by  firing  a  smoke  puff  from  a 
Verey  pistol,  and  tracing  its  subsequent  path  by  means  of  a 
camera  obscura,  the  velocity  of  the  wind  being  assumed  constant 
along  the  course.  In  order  to  increase  the  accuracy  of  this  test, 
the  machine  flies  up  and  down  the  course  se\7eral  times. 

A  third  method  is  to  apply  the  camera  obscura  observation 
of  the  smoke  puff  to  the  observation  of  the  flight  of  the  machine 
itself. 

Rate  of  Climb  Test.— The  measurement  of  rate  of  climb 
is  generally  carried  out  by  observing  the  time  taken  to  climb  a 
given  distance,  this  distance  being  measured  by  means  of  an 
aneroid  barometer.  This  instrument  is  really  a  pressure  indi- 


PERFORMANCE  397 

cator,  and  measures  the  height  in  terms  of  the  variation  of 
pressure  due  to  change  of  altitude,  the  scale  of  the  instrument 
being  graduated  to  read  height  instead  of  pressure. 

Theory  of  the  Aneroid  Barometer.  —Let  P  and  Q  be  two 
.points  at  altitudes  h  and  h"  respectively  (see  Fig.  283).  It  is 
required  to  find  the  vertical  height  between  them  in  terms  of 
the  pressure  of  the  atmosphere. 

Take  two  points,  A  and  B,  situated  very  close  to  one  another, 
and  let  the  pressure  per  square  inch  at  A  be  /  and  at  B  be 
p  -f-  dp,  and  the  distance  between  A  and  B  be  d x.  Then  the 
increase  in  pressure  at  B  is  due  to  the  weight  of  the  small  column 
of  air,  of  height  dx  and  one  square  inch  in  cross  section,  that  is 

(p  +  dp}  -  p  +  pgdx  =  o 

where  p  is  the  mean  density  of  the  air  between  A  and  B.  If  the 
air  be  at  constant  temperature,  the  density  is  proportional  to 
the  pressure,  that  is 

P  oc/ 
Or        p  =  kp 

Substituting  in  equation  above 

dp  +  kp  gdx  =  o 

Or         dp 

—  -¥    kgdx    =  o 

P 

Integrating 

l°ge/  +      kgx      =  constant. 

If/'  be  the  pressure  at  P,  and/"  the  pressure  at  Q,  then 

loge/    +    kgk'    =    loge/'    +    kgk" 

Or  h' -  h"  = -±-\o&£- 

kg        p       rormula  101; 

That  is,  the  difference  in  altitude  is  equal  to  difference  between 
the  Napierian  logarithms  of  the  pressures  multiplied  by  a 
constant. 

Formula  101  has  been  obtained  on  the  assumption  that  the 
temperature  of  the  atmosphere  remains  constant,  but  since  this 
is  not  the  case,  it  is  necessary  to  introduce  a  temperature  cor- 
rection factor  for  the  aneroid  readings,  unless  a  temperature 
correction  device  has  been  incorporated  in  the  instrument. 


AEROPLANE    DESIGN 


The  aneroid  or  altimeter  (see  Fig.  284)  consists  essentially 
of  a  shallow  corrugated  metal  drum  from  which  the  air  has 
been  exhausted.  A  strong  spring  attached  to  the  top  of  the 
drum  enables  it  to  withstand  the  atmospheric  pressure  tending  to 
crush  it.  With  increase  of  altitude  the  pressure  on  the  exhausted 
chamber  diminishes,  thereby  allowing  the  spring  to  distort  it. 


Needle 


BaOance 
Weight 


FIG.  284. — Aneroid  Altimeter. 


The  ensuing  movement  of  the  drum  is  communicated  to  the 
indicator  by  means  of  a  delicate  mechanism  of  the  nature  shown 
in  Fig.  284. 

In  order  to  provide  for  the  variation  of  atmospheric  pressure 
at  ground  level,  a  thumbscrew  is  provided  whereby  the  needle 
can  be  adjusted  to  zero  position  on  the  scale.  The  variation  in 
temperature  is  allowed  for  by  means  of  a  steel  and  brass 


To 


FIG.  285. 

compensating  device  fixed  to  one  of  the  levers.  The  unequal 
expansions  of  these  two  metals  provides  the  necessary 
correction. 

Measurement  of  Rate  of  Climb. — This  measurement  is 
made  in  several  different  ways.  Either  the  time  to  climb  a 
definite  height,  or  the  height  attained  in  a  definite  time,  may 
be  measured.  The  horizontal  speed  is  varied  over  definite  steps 
ranging  from  the  minimum  to  the  maximum  possible  at  the 
altitude  in  question,  and  the  rate  of  climb  measured  in  each 
case  with  the  engine  at  full  throttle.  By  plotting  the  results 
obtained  it  is  easily  seen  at  which  speed  the  maximum  climb  is 


PERFORMANCE 


399 


attained  and  the  corresponding  value.  An  instrument  called  a 
climb-meter  has  also  been  devised.  It  consists  of  a  Dewar 
vacuum  flask,  which  communicates  with  the  outer  air  through 
a  piece  of  glass  tubing  which  is  arranged  with  an  air  trap  at 

Longitudinal  Clinometer. 


Altitude 
Recorder. 


Airspeed 
Indicator. 


'  Time  of 
Trip'  Clock. 


Revolution 
Indicator. 


Lateral  Clinometer. 
Fig.  286. — Aviation  Instrument  Board. 

(By  iwirtesy  of  Messrs.  S.  Smith  &  Sons,  Ltd.] 


each  end.  The  trap  serves  to  limit  the  path  of  a  small  drop  of 
liquid,  which  acts  as  an  air  seal  when  the  internal  and  external 
air  pressures  are  equal.  (See  Fig.  285.)  A  manometer  tube 
connected  to  the  flask  serves  to  indicate  the  difference  between 
the  internal  pressure  and  that  of  the  atmosphere.  As  soon  as 


400  AEROPLANE    DESIGN 

the  machine  commences  to  climb,  the  pressure  of  the  atmosphere 
is  diminished,  and  the  greater  pressure  inside  the  flask  forces 
the  drop  of  liquid  to  the  trap  furthest  away  from  it,  thus 
allowing  the  air  to  escape.  During  climbing,  therefore,  the 
internal  pressure  always  tends  to  be  greater  than  the  external, 
and  the  enclosed  air  escapes  through  the  trap.  When  the 
machine  is  climbing  at  its  maximum  rate  the  difference  of 
pressure  between  the  inside  and  outside  of  the  flask  is  greatest, 
and  this  will  be  indicated  by  the  maximum  difference  in  level 
of  the  manometer  tube  attached  to  the  flask.  The  pilot  there- 
fore adjusts  the  attitude  of  his  machine  until  this  condition  is 
attained.  To  indicate  when  the  machine  is  flying  horizontally 
a  Statoscope  is  used.  This  instrument  is  similar  in  principle 
to  the  Climbmeter.  In  this  case,  however,  the  pilot  will  adjust 
the  drop  of  liquid  (Fig.  285)  until  it  is  in  the  central  position. 

From  the  foregoing  remarks  it  will  be  seen  that  the  number 
of  instruments  requiring  attention  on  the  part  of  the  pilot  for 
flying  the  machine  are  fairly  numerous,  in  addition  to  which 
further  instruments  are  required  for  controlling  the  engine.  In 
order  to  arrange  these  instruments  conveniently  for  use  and 
observation,  various  types  of  instrument  boards  have  been  de- 
vised. Fig.  286  shows  an  instrument  board  designed  by  Messrs. 
S.  Smith  &  Sons. 

A  summary  of  the  various  measurements  to  be  made  in  the 
test  of  performance  may  now  be  given. 

1.  Flying  speed. 

(a)  The  engine  revolutions  and  the  airspeed  are  noted 
when  flying  level  with  full  throttle. 

(b)  From  the  aneroid   reading  and  temperature  obser- 
vation at  each  height  the  density  is  obtained.     The 
reading  of  the  airspeed  indicator  is  then  corrected  by 
dividing  by  the  square  root  of  the  density. 

(c)  These   corrected    results    are    plotted    against    the 
average  height  in  feet.     An  example  of  such  a  test 
is  given  in  Tables  LX.  and  LXI. 

2.  Rate  of  climb. 

(a)  The   aneroid    height    every     1000  feet  is    observed, 
together  with  the  corresponding  times  from  the  start. 

(b)  The  observed  times  are  then  plotted  against  aneroid 
heights.     From  the  curve  obtained,  the  rate  of  climb 
at  any  point  can  be  obtained  from  the  tangent  to  the 
curve  at  that  point. 

Table  LXII.  gives  the  results  of  a  Rate  of  Climb  Test. 


PERFORMANCE 


401 


TABLE  LX. — CALIBRATION  OF  AN  AIRSPEED  INDICATOR  BY 
DIRECT  TEST. 


•a 

§ 

•a 

c 

c 
o 

u 

-C 

M 

I* 

£ 

tj 

£ 

<u 

el 

•a 

'5 

, 

0 

c 

3 
Qti 

Measured 
speed  m.p 

Measured 
speed. 

1 

•a 

c 

i 

Corrected 
speed. 

Observed 
(aneroid). 

Observed 
temperatu 

a 
•d 

§£ 
<55  g 

5-0-o 

Observed 
speed. 

Airspeed. 

>-, 

c 

0) 

1 

Correction 

I 

59'I 

31-0 

i6i'5° 

Sg-2 

5100 

31-0° 

0-879 

80 

83-6 

3-6 

o 

12.3-4 

28-6 

5*5° 

937 

5100 

31-0° 

0-879 

8< 

/ 

•8 

2-8 

3 

62*0 

32-3 

168-5° 

93-« 

5050 

31-0° 

0-881 

8S 

88-1 

3'i 

4 

1247 

32-3 

2I'0° 

95  6 

5000 

31-0° 

0-882 

86 

8* 

!-8 

2-8 

Mean  =    3*1 


TABLE  LXI. — AIRSPEED  AT  HEIGHTS. 


j. 

C 

i   e-f 

.£?!» 

JO 

o 

^  '53 

r;            iti, 

r-}                    1>   <U 

C  ^3 

S.-S 

It' 

o 

1  . 

o 

£  ^-t.        oj  •*-> 

fit  •*-*          c/J  rt 

1 

11 

is. 

£•55 

•-S 

c  £      -SB 

g 

V-i  C 

^  S2 

O  -£^ 

o  g 

^  'ex 

<£    o  SL 

Q 

p-s 

O'S 

h  « 

&  g 

3000 

39° 

'935 

2900 

95 

98 

ioi'5 

1280 

3000 

103-0 

1290 

5000 

35° 

•875 

4900 

93 

96 

1.  02  '5 

1280 

6500 

100-5 

1250 

7000 

30°   -821 

6900 

88 

91 

100-5 

1240 

9200 

24°   -767 

9000 

81 

84 

96*0 

1220 

10000 

96'5 

I2I5 

10800 

I9°   '731 

10400 

80 

83 

97-0 

1220 

12800 

17° 

•682 

12600 

72 

75 

92*0 

1200 

13000 

94-0 

1180 

13800      12°    '664 

13400 

68 

72 

88-5 

1180 

! 
1 

15000 

86-0 

1  1  60 

15200 

8   -636 

14800 

64 

69 

86-5 

1  1  60 

i          i 

D  I) 


4O2 


AEROPLANE    DESIGN 


TABLE  LXII. — RATE  OF  CLIMB  TEST. 


Height  in  feet 
aneroid. 

Observed  tem- 
perature (F.). 

%  Standard 
density. 

Observed  time 
(minutes). 

Ratt  of  climb 
feet 
per  minute. 

1000 

37° 

lOI'O 

I  '00 

814 

2000 

38° 

97-2 

2'10 

7l8 

3000 

36° 

94.2 

370 

622 

4000 

36° 

907 

5  '40 

544 

5000 

36° 

87-4 

7-25 

495 

6000 

33° 

847 

9'4 

435 

7000 

3°° 

82-1 

11-9 

389 

8000 

26° 

79*9 

14*25 

347 

9000 

26° 

77-6 

17*00 

312 

IOOOO 

23° 

747 

20-25 

294 

1  1  000 

21° 

72-2 

23-6 

264 

12000 

20° 

69-8 

27-4 

216 

13000 

17° 

677 

3r9 

182 

14000 

12° 

65*9 

37'9 

139 

15000 

8° 

64-1 

45'25 

IOI 

CHAPTER  XIII. 
GENERAL  LAY-OUT  OF  MACHINES. 

The  process  of  laying  out  an  aeroplane  varies  consider- 
ably in  different  drawing  offices,  some  of  the  methods  adopted 
being  excellent  examples  of  correct  procedure,  while  in  many 
other  cases  'rule-of-thumb'  ideas  prevail.  As  a  painful  illus- 
tration of  the  latter  method,  or  perhaps  more  correctly  lack  of 
method,  we  outline  how  a  machine  is  designed  in  an  aeronautical 
drawing  office  with  which  we  are  acquainted. 

The  designer  decides  upon  a  new  machine,  and  guesses  at 
the  complete  weight.  The  area  of  the  wings  is  then  obtained 
by  dividing  this  weight  by  seven,  probably  in  order  to  give 
an  approximate  loading  of  seven  pounds  per  square  foot.  A 
draughtsman  is  then  summoned,  and  instructed  to  get  out  a 
side  elevation,  and  sometimes  a  plan,  being  told  the  type  of 
engine,  the  number  of  passengers,  the  quantity  of  petrol  to  be 
canied,  the  stagger  and  the  chord.  The  draughtsman  is  then 
compelled  to  arrange  his  weights  by  a  process  of  wangling,  and 
usually  puts  in  the  size  of  the  fin,  rudder,  and  tail  plane  by  '  eye/ 
This  drawing  is  then  passed  on  to  the  fuselage  expert,  who  runs 
out  a  drawing  of  this  unit,  while  the  first  draughtsman  stresses 
the  wings  and  settles  the  section,  spars,  and  other  details.  The 
whole  staff  is  then  employed  on  preparing  detail  drawings  for 
the  shops,  and  on  completion  the  building  of  the  first  machine  is 
commenced.  At  this  stage  the  designer  has  a  walk  round,  and 
promptly  proceeds  to  alter  the  majority  of  the  details,  fresh 
drawings  are  prepared,  and  the  process  is  repeated.  After 
several  alterations  the  machine  approaches  completion,  and  then 
possibly  a  general  arrangement  is  prepared.  In  the  hands  of  a 
genius  such  a  manner  of  lay-out  may  produce  excellent  results, 
but  it  is  neither  scientific  nor  up-to-date. 

In  order  to  produce  an  economical,  successful,  and  scientific 
design,  requiring  very  few  alterations  while  in  course  of  manu- 
facture in  the  shops,  careful  attention  mu>t  be  paid  to  the  points 
outlined  in  the  preceding  chapters,  and  we  will  now  show  how 
to  apply  these  chapters  to  the  design  of  machines.  For  the 
purpose  of  illustration  we  will  consider  the  des;gn  of  a  biplane 
having  a  speed  of  120  miles  per  hour  at  io,oco  feet,  a  landing 
speed  of  50  miles  per  hour,  a  radius  of  action  of  480  miles,  and 
capable  of  carrying  at  least  500  Ibs.  of  useful  load,  excluding 
fuel.  Referring  to  Table  XL.,  we  see  that  the  useful  load  repre- 


AEROPLANE    DESIGN 

sents  approximately   14%   of  the  total  weight  of  the  machine, 
so  that  we  have 

Total  weight  =  x  500 

=  3570  Ibs. 

For  the  present  this  weight  will  be  taken  as  3500  Ibs.,  and 
at  once  from  Table  XL.  we  get  the  following  estimate  of  the 
weights  of  the  various  components  : 

I.    THE  POWER  PLANT. 

(a)  Engine 

(b)  Kadiators 

(c)  Cooling  water   ... 

(d)  Tanks,cetc 

(e)  Airscrew,  etc.    ... 

II.   THE  GLIDER. 

(a)  The  wings 

(b}  The  wing  bracing 

(fj   The  tail  unit     ... 

(</)  The  body          ...    ,     ... 

(e)   The  chassis 

III.  USEFUL  LOAD. 

(a)  Fuel       ... 

(b)  Passengers,  etc. 

IV.  Instruments,  etc. 

Total  weight  35°° 

Before  proceeding  further  it  is  necessary  to  determine  whether 
the  estimated  weight  of  power  plant  will  permit  of  an  engine  of 
sufficient  power  to  give  the  required  performance.  This  brings 
us  to  a  consideration  of  the  supporting  surfaces. 

In  Chapter  III.,  on  wing  sections,  we  saw  that  the  essential 
features  of  a  wing  section,  to  give  a  good  range  of  speed,  were 
as  follows  : 

(a)  A  high  value  of  the  maximum  lift  coefficient  (Ky  max.) ; 

(£)  At  small  angles  of  incidence  the  value  of  Ky  may  be 
small,  but  the  value  of  the  L/D  ratio  must  be  large. 

The  maximum  landing  speed  required  will  determine  the 
first  of  these  requirements,  while  the  relative  merits  of  various 
aerofoils,  in  order  to  fulfil  the  second  requirement  to  the  best 
advantage,  may  be  investigated  as  follows.  The  most  efficient 


GENERAL   LAY-OUT   OF   MACHINES  405 

aerofoil  at  the  speed  required  will  be  the  one  which  offers  the 
least  resistance  (drag).  The  lift  on  the  wings  is  equal  to  the 
weight  of  the  machine,  and  is  therefore  the  same  on  each  aero- 
foil section.  The  best  type  of  aerofoil  to  use,  therefore,  is  the 
one  which  has  the  highest  value  of  L/D  at  the  required  speed  *  V  ', 
that  is,  at  a  value  of 

Ky  =  Ky  (max.)  x  f  — ^ 

where  VL  is  the  landing  speed. 

By  examining  the  characteristics  of  a  number  of  aerofoils 
by  means  of  this  equation,  the  most  suitable  section  from  a 
theoretical  standpoint  is  determined.  Practical  considerations, 
such  as  ease  of  manufacture  of  ribs,  spars,  etc.,  may  lead  to 
modification  in  the  type  selected,  but  the  underlying  principles 
of  wing  design  should  be  based  on  such  an  investigation. 

The  Wing  Sections  shown  graphically  at  the  conclusion  of 
Chapter  III.  have  been  investigated  with  this  end  in  view,  and 
Fig.  76  (Section  No.  10)  represents  the  section  and  aerodynamic 
characteristics  most  suitable  for  the  present  design. 

It  will  be  seen  that  the  maximum  value  of  Ky  is  O'63-  For 
a  landing  speed  of  50  m.p.h.  the  necessary  wing  area  is  given  by 
the  equation 

W 


Area  = 

£  Ky  V* 
g 

35°° 


•00237  x  0-63  x  73-3  x  73-3 
=  435  square  feet. 

Allowing  for  loss  of  efficiency  of  aerofoil  due  to  the  biplane 
arrangement,  and  taking  a  factor  of  '8,  we  find  that  the  area 
of  supporting  surface  required 

=  540  square  feet. 

Having  decided  upon  the  most  suitable  wing  section,  we  are 
now  in  a  position  to  form  an  estimate  as  to  the  engine  horse- 
power necessary  to  enable  the  required  performance  to  be 
obtained. 

This  can  be  roughly  investigated  as  follows  :  The  value  of 
the  lift  coefficient  required  at  a  speed  of  120  m.p.h.  when  flying 
at  10,000  feet,  where  the  value  of  p/g  is  -00177, 

35°° 


•00177  x  540  x   176  x   176 
•118 


406  AEROPLANE    DESIGN 

On  looking-  at  our  curve  of  aerofoil  characteristics,  we  see 
that  for  a  value  of  Ky  =  Ti8  the  corresponding  L/D  ratio  is 
approximately  9'6,  hence  the  drag  of  the  wings  under  these 
conditions  is  3500/9*6  =  365  Ibs. 

For  the  most  economical  speed  of  flight,  namely,  that  cor- 
responding to  maximum  L/D,  the  wing  and  body  resistance  are 
approximately  equal.  Upon  this  basis  the  total  resistance  of 
the  machine  will  be  twice  that  of  the  wings,  that  is,  730  Ibs. 
This  resistance  must  be  balanced  by  the  thrust  of  the  airscrew, 
that  is, 

H.P.  of  engine  x  550  x  efficiency  of  airscrew 
-.*  Maximum  flying  speed 

whence  horse-power  of  engine  required 

=  73Q  x  176 
550  x  o'8 

=  292 

The  assumption  made  above,  that  the  resistance  of  the  body 
is  equal  to  that  of  the  wings,  is  approximately  true  only  for  the 
most  economical  speed  of  flight,  and  for  speeds  greater  than  this 
the  body  resistance  will  probably  be  greater  than  that  of  the 
wings  ;  hence  the  total  resistance  assumed  above  is  somewhat 
less  than  the  true  value  at  top  speed.  It  is  therefore  advisable 
to  insert  an  engine  possessing  greater  power  than  that  given 
above  in  order  to  be  sure  of  obtaining  the  desired  performance, 
and  to  have  a  reserve  of  power  for  unexpected  contingencies. 

Reference  to  Table  XLI.  shows  that  the  most  suitable  water- 
cooled  engines  are  the  350  h.p.  Rolls-Royce  and  the  300  h.p. 
Hispano-Suiza ;  whereas,  if  an  air-cooled  engine  were  to  be 
adopted,  the  320  h.p.  A.B.C.  Dragonfly  should  be  sufficient. 

Using  the  particulars  given  in  Table  XLI.,  the  following 
table  showing  the  relative  merits  of  these  three  engines  for  the 
purpose  of  the  present  design  can  be  prepared  : 

350R.-R.          3ooH.-S.         320  A.B.C. 

Ibs.  Ibs.  Ibs. 

Weight  of  power  unit         ...       933  ...       596  ...       600 

Weight  of  fuel  for  4  hours...       740  ...      690  ;..      742 

Total  weight  ...     1673       ...     1286       ...     1342 

An  examination  of  these  particulars  shows  that  the  A.B.C. 
Dragonfly  engine  is  the  most  suitable  for  our  purpose,  there 
being  the  additional  advantage  that  it  is  an  air-cooled  engine, 
and  therefore  the  weight  allowed  for  radiator  and  cooling  water 
will  be  available  for  useful  load. 

If  this  machine  were  intended  for  righting  purposes  it  would 


GENERAL    LAY-OUT   OF    MACHINES  407 

perhaps  be  advisable  to  use  the  350  Rolls-Royce,  in  order  to 
have  a  reserve  of  power  for  emergencies,  and  in  order  to  ba 
quite  sure  of  obtaining  the  desired  performance. 

Having  checked  the  estimated  weights  of  the  power  plant, 
attention  must  be  turned  to  the  determination  of  the  principal 
dimensions  of  the  machine. 

The  total  wing  area  having  been  already  fixed,  the  next  step 
is  to  decide  upon  the  span  and  the  chord.  A  suitable  aspect 
ratio  is  7,  so  that  we  have 

S  =  7C     (i.) 
S  x  C  =  540     (ii.) 


z  o    -^    v^    — 

Solving  these  equations,  we  have 

Q     = 


S    =  44  feet. 
C  -  6-25  feet. 

In  order  to  allow  for  '  end  effect '  and  loss  of  centre  portion  we 
will  make  span  45  feet,  and  chord  6  ft.  3  in. 

GAP.— It  is  next  necessary  to  fix  the  amount  of  gap  re- 
quired. General  aeronautical  practice  to-day  makes  the  gap 
equal  to  the  chord.  When  the  gap  is  equal  to  the  chord  the 
loss  in  efficiency  is  equal  to  '8  which  was  the  figure  adopted 
in  calculating  the  extra  area  required  on  account  of  the  biplane 
arrangement.  We  shall  therefore  make,  the  gap  equal  to  the 
chord,  that  is  equal  to  6  ft.  3  ins. 

STAGGER. — For  fighting  purposes  a  good  field  of  view  is 
essential,  and  as  this  is  also  a  desirable  attribute  for  general 
utility  purposes  we  shall  adopt  a  small  amount  of  positive 
stagger,  say  one  foot.  When  we  come  to  consider  the  position 
of  the  centre  of  gravity  of  the  machine  at  a  later  stage  it  may  be 
necessary  to  modify  this  amount. 

DIHEDRAL. — Considerations  relating  to  lateral  stability  make 
it  advisable  to  give  a  small  dihedral  angle  to  the  wings.  A 
dihedral  angle  of  3°  will  therefore  be  adopted  for  the  purpose  of 
preliminary  design. 

The  next  step  is  to  settle  the  length  of  the  fuselage  required. 
Generally  speaking,  it  is  found  that  in  order  to  obtain  a 
reasonable  degree  of  controllability,  the  distance  from  the  C.G.  of 
the  machine  to  the  C.P.  of  the  tail  plane  varies  from  one-half  to 
one-third  of  the  wing  span.  The  span  of  our  machine  is  45  feet, 
hence  a  length  of  fuselage  of  16  feet  between  the  trailing  edge 
of  the  lower  wing  and  the  sternpost  should  be  sufficient. 

CONTROLS. — The  next  item  in  the, design  is  the  size  of  the 
lateral  and  longitudinal  control  surfaces.  An  empirical  formula 
may  be  used  to  arrive  at  a  first  estimate  of  the  size  of  the  tail- 
plane  and  elevator,  or  recourse  may  be  had  to  an  investigation 


4o8  AEROPLANE    DESIGN 

into  the  sizes  adopted  on  similar  machines.     For  our  purpose  we 
will  use  the  following  formula  : 

•4  x  (area  of  wings  x  chord) 
ftail  Plane    =  Dist.  between  C.P.  of  wings  and  tail  plane 

=  '4  x  54Q  x  6-25 
16 

=  70  square  feet  approx. 

We  shall  divide  this  area  as  follows : 

Area  of  tail  plane,  40  square  feet. 
Area  of  elevators,  30  square  feet. 

A  common  aspect  ratio  for  the  combined  tail  member  is 
three,  which  gives  us  approximately  14  foot  span  and  5  foot 
chord.  The  section  should  be  symmetrical  and  of  sufficient 
depth  to  allow  of  a  suitable  spar. 

RUDDER  AND  FlN. — The  correct  area  of  the  rudder  and  fin 
is  bound  up  with  the  question  of  the  lateral  stability  of  the 
machine,  and  as  we  are  not  yet  in  a  position  to  investigate  this 
mathematically  or  experimentally,  it  is  advisable  to  fall  back 
upon  the  size  adopted  in  existing  machines  of  similar  type  and 
similar  dimensions.  A  suitable  area  of  fin  will  be  12  square 
feet,  and  of  rudder  18  square  feet. 

An  alternative  and  very  useful  method  of  arriving  at  a  rough 
estimate  of  the  fin  and  rubber  area  required  is  as  follows :  A 
side  view  of  the  machine  is  drawn  to  scale  on  a  piece  of  stiff 
cardboard.  The  outline  is  then  cut  out  with  a  sharp  knife, 
leaving  a  fairly  wide  margin  round  the  proposed  shape  of  the  fin 
and  rudder.  The  cardboard  outline  is  then  balanced  on  the 
edge  of  a  knife  placed  perpendicular  to  the  longitudinal  axis  of 
the  machine,  and  the  margin  round  the  fin  and  rudder  trimmed 
until  balance  is  obtained  at  a  distance  of  about  3"  (to  the  scale 
used  for  the  model  outline)  behind  the  desired  position  of  the 
centre  of  gravity  of  the  machine.  The  weight  on  each  side  of 
the  knife-edge  approximates  to  the  side  force  of  the  wind  on 
the  machine  and  thus  gives  a  rough  measure  of  the  fin  area 
required  for  stability. 

It  should  be  carefully  noted  that  these  areas  for  control 
surfaces  are  provisional,  and  before  adopting  them  in  the  final 
design  every  effort  must  be  made  to  investigate  the  stability  of 
the  machine  according  to  the  mathematical  theory  outlined 
in  Chapter  X. 

General  Arrangement. — We  are  now  sufficiently  advanced 
to  lay  out  a  scheme  for  the  G.A.  of  the  machine  (see  Fig.  287). 
The  wings  must  first  be  drawn  with  their  correct  relative 


GENERAL   LAY-OUT   OF   MACHINES 


409. 


positions  of  gap,  stagger,  etc.  It  is  customary  to  give  them  an 
initial  angle  of  incidence  with  reference  to  the  datum  line  of  the 
fuselage,  a  common  angle  being  3°.  The  next  step  is  to  de- 
termine the  mean  chord  of  the  biplane  arrangement  as  set  out  in 
Chapter  XI.  The  position  of  the  mean  chord  enables  the  wing 
structure  to  be  arranged  relative  to  the  remainder  of  the 
machine,  as  it  is  usual  to  distribute  the  weight  of  the  machine 


FIG.  287. — Lay-out  of  Aeroplane. 

in  such  a  manner  that  the  C.G.  of  the  whole  machine  is  at  a 
distance  of  '35  x  mean  chord  from  its  leading  edge  longitu- 
dinally and  a  few  inches  below  vertically.  This  point  is  there- 
fore marked  on  the  side  view  of  the  wing  structure,  and  the 
position  of  the  C.G.  of  the  remainder  of  the  machine  determined 
as  under.  This  entails  the  drawing  out  of  the  fuselage  and  tail 
unit  and  the  fixing  of  the  various  weights  in  their  respective 
positions.  Variable  weights  such  as  oil,  fuel,  passengers,  etc ,, 


410  AEROPLANE   DESIGN 

should  be  placed  as  near  to  the  C.G.  as  possible.  The  cross 
section  of  the  fuselage  will  be  governed  by  the  space  necessary 
to  house  the  engine,  tanks,  pilot,  and  passenger.  Having  settled 
these  points  a  preliminary  '  balancing  up '  can  be  completed. 

For  this  purpose  it  is  customary  to  take  moments  about  a 
fixed  datum  line.  A  convenient  line  for  this  purpose  is  the 
vertical  line  through  the  nose  of  the  machine.  The  estimated 
weight  is  then  multiplied  by  its  distance  from  this  datum  line, 
and  thus  the  moment  of  each  weight  about  this  line  is  obtained. 
The  sum  of  all  these  moments  divided  by  the  weight  of  the 
complete  machine  will  give  the  position  of  the  C.G.  relative  to 
the  datum  line  selected.  The  work  should  be  arranged  in 
tabular  form  as  shown  in  Table  LXIII. 

TABLE  LXIII. —DETERMINATION  OF  THE  POSITION  OF  THE 
CENTRE  OF  GRAVITY. 

Description  of  part.  Weight.  Distance  from  datum.  Moment. 

Ibs.  feet. 

Airscrew,  etc.   ...            87*5  ..  i'o  ...              87*5 

Engine...         ...  600*0  ...  3*0  ...  iSoo'o 

Fuel      742  ...  7-5  ...  5565*0 

Tanks 105  7-5                       T&T5 

Fuselage           ...  455  ...  11*0  ...  5°°5 

Pilot      180  8-0  1440 

Passenger         ...  180  ...  12*5  ...  2250 

Tail  unit          ...            70  ...  28*0  ...  1963 

Instruments      ...            35  ...  7'o  ...            245 

2454-5  19140 

Distance  of  C.G.  from  the  datum  line 

=  x  =  7 '8  feet  from  nose  of  machine. 

It  will  be  noticed  that  the  chassis  has  been  omitted  in  the 
above  estimate.  This  is  because  its  position  is  determined  from 
the  estimated  C.G.  in  the  manner  set  forth  in  Chapter  VIII., 
and  since  this  component  acts  close  to  the  final  position  of  the 
C.G.  it  can  be  neglected  for  the  moment,  as  it  will  be  partly 
balanced  by  the  wings,  which  have  also  been  omitted. 

The  next  step  is  to  superpose  the  drawing  of  the  wing  struc- 
ture upon  that  of  the  body  so  that  the  longitudinal  position  of 
the  C.G.  of  the  machine  is  at  '35  times  the  mean  chord,  and 
.also  with  the  bottom  of  the  fuselage  resting  on  the  lower  plane. 

The  chassis  can  now  be  fixed  in  position  relative  to  the  C.G. 

A  second  balance-up  should  next  be  undertaken,  the  wings 
and  chassis  being  included  this  time  and  the  position  of  the  C.G. 
determined  both  horizontally  and  vertically.  This  is  set  out  in 
Table  LXIV. 


GENERAL    LAY-OUT   OF    MACHINES  411 

As  well  as  the  G.A.  drawing  of  the  complete  machine, 
general  arrangement  drawings  of  the  different  units  should  also 
be  prepared,  each  preferably  by  an  expert  designer  of  each 
item,  and  the  various  details  should  be  handed  out  to  different 
draughtsmen  to  prepare.  A  standard  size  should  be  adopted 
for  the  G.A.  drawings  of  complete  machines,  and  another  size 
for  the  G.A.  drawings  of  the  different  units  ;  while  the  detail 
drawings  should  be  neatly  arranged  upon  sheets  of  the  same 
size  as  the  latter  drawings  if  only  one  machine  is  being  built, 
while  for  quantity  production  it  is  advisable  to  have  a  separate 
sheet  for  each  detail.  The  G.A.  drawing  of  the  complete 
machine  should  bear  the  serial  number  of  the  design,  and  the 
other  sheets  should  all  bear  this  number,  and  in  addition  should 
be  lettered  and  numbered  according  to  some  systematic  plan. 
The  following  scheme  of  lettering,  being  practically  self- 
explanatory,  has  much  to  recommend  it  :— 

Name  of  unit.  Distinguishing  letter. 

Fuselage  F 

Tail  skid  F  — TS 

Tanks „£.       F  — T 

Engine  installation       ...          ...          ...          ...  F — El 

Fuselage,  stress  diagrams        ...          F — SD 

Wings \V 

Wings,  stress  diagrams  W — SD 

I nterplane  struts          W — S 

Wings,  wiring '";..*:.'       ...  W— W 

Tail-plane  unit  TP 

Chassis U 

Chassis,  stress  diagrams U — SD 

Controls  ...          ...  •       ...          ...          ...  C 

Engine  controls  ...          ...          ...          ...  C — E 

Instrument  board        ...          ...          ...          ...  I 

Part  lists          PL 

Detail  sheets  belonging  to  each  series  will  be  consecutively 
•numbered,  the  G.A.  sheet  of  the  series  being  number  one,  of 
course.  For  example,  the  G.A.  sheet  of  the  tail-plane  unit  for 
a  machine  whose  design  number  is  55  would  be  numbered 
55 — TP — i,  and  the  fifth  sheet  of  details  of  the  same  tail-plane 
unit  would  be  numbered  55 — TP — 5. 

The  position  of  the  wing  structure  relative  to  the  fuselage 
having  now  been  fixed,  the  side  view  of  the  machine  can  be 
completed.  It  is  advisable  to  make  this  arrangement  as  detailed 
as  possible.  The  main  dimensions  should  be  inserted  in  some 
decimal  unit  in  order  to  facilitate  calculations,  and  great  care 
should  be  taken  to  see  that  the  drawing  is  correct  to  scale. 

The  fuselage  between  the  rear  chassis  struts  and  the  nose  of 


4I2 


AEROPLANE    DESIGN 


the  machine  should  be  amply  strong,  and  the  engine-bearers- 
should  be  supported  on  stout  ribs  built  up  of  three-ply  wood. 
Longerons  should  be  made  of  ash  about  r-J"  square,  tapering  to- 
about  i"  square  at  the  sternpost. 

The   fuel    and  oil  tanks   should   be    drawn    in  their  correct 
positions,  and  provision  made  for  strapping  to  the  fuselage. 


FIG.  274. — Tail  Unit  Components.     (See  also  p.  379.) 


The  engine  and  control  connections  may  with  advantage  be 
drawn  in  red  ink.  A  strong  cross  strut  should  be  introduced  to- 
take  the  thrust  of  the  rudder  bar  ;  and  footboards  run  in  for  the 
pilot  and  passenger.  About  ij"  diameter  tube  will  be  suitable 
for  the  control  lever. 


GENERAL   LAY-OUT   OF    MACHINES  413 

The  instrument  board  position  should  be  drawn  in,  allowing 
ample  clearance  for  the  control  lever  and  a  long-legged  pilot's 
knees.  A  low  shield  affixed  to  the  fuselage,  and  streamlining 
the  forward  end  of  the  openings  to  the  cockpits,  will  spill  the  air 
•over  these  openings,  and  thus  reduce  resistance  in  the  open 
design.  These  openings  may  be  cut  out  of  thin  three-ply  wood. 
Elsewhere  three-ply  should  be  avoided  on  account  of  its  weight 
(except  around  the  engine  forward,  where  it  may  be  used  in 
place  of  bracing  wires),  and  also  on  account  of  its  dangerous 
splinters  in  the  case  of  a  crash. 

Join  the  longerons  together  forward  by  means  of  a  nose- 
plate  made  of  sheet  steel  of  about  No.  16  S.W.G.,  lightened  out 
wherever  possible,  and  with  its  edges  turned  up  to  give  stiffness 
and  to  act  as  corner  sockets.  A  ball-bearing  for  the  airscrew 
shaft  may  be  introduced  if  required  on  this  plate.  The  longerons 
aft  should  be  joined  together  in  pairs  and  attached  to  the  stern- 
post.  The  sternpost  may  be  either  tubular  or  of  wood,  and  the 
rudder  should  be  hinged  to  it.  The  main  spar  of  the  tail  plane 
may  also  be  attached  at  this  point,  the  front  spar  being  attached 
to  a  vertical  strut  in  the  fuselage. 

The  elevators  are  hinged  to  the  rear  spar  of  the  tail  plane, 
and  10  mm.  tubing  may  be  used  for  the  trailing  edges  of 
elevators  and  rudder.  Cable  levers  should  be  short  and  of 
streamline  form. 

The  sternpost  should  be  streamlined  above  the  fuselage  with 
the  fin,  and  below  the  fuselage  should  be  used  for  attachment  of 
a  small  tail  skid.  The  static  moment  on  this  tail  skid  may  be 
determined  by  taking  moments.  Rule  a  line  from  the  base  of 
the  wheels  to  the  end  of  the  skid  and  project  the  position  of  the 
C.G.  of  the  whole  machine  on  to  this  line,  and  the  moment  at 
once  follows.  The  tail  skid  should  be  designed  to  withstand  a 
load  several  times  greater  than  this  static  load  in  order  that  it- 
may  survive  the  shock  of  a  bad  bump.  It  will  be  advisable  to 
recalculate  the  position  of  the  C.G.  of  the  machine.  If  it  is 
found  that  the  machine  is  coming  out  nose-heavy — that  is,  that 
the  C.G.  is  too  far  forward — then  the  balance  may  be  adjusted 
by  moving  the  engine  back.  On  the  other  hand,  if  the  machine 
is  coming  out  tail-heavy,  then  the  engine  may  be  placed  further 
forward.  For  example  : 

Let       a  be  distance  of  the  C.G.  in  front  of  the  required  position 

W  be  the  total  weight  of  the  machine 

w  be  the  weight  of  the  engine  or  other  parts  to  be  moved 

;v  be  the  distance  required 
then     w  x  =  W  a 
or         x      =  W  a\w 


414 


AEROPLANE    DESIGN 

TABLE  LXIV.— BALANCING. 


ESTIMATED. 

MEASURED. 

Distance 

from 

Item. 

Weight. 

nose  of 
machine. 

Moment. 
W  x  D. 

Longi- 
tudinal. 

Weight. 
W. 

Distance 
D. 

Moment. 
WxD. 

Ft. 

D. 

Airscrew   ... 

87-5 

I'O 

87-5 

Engine 

600 

3"o 

1800 

.'.  Long1 

Fuel 
Tanks 
Chassis 

742 
105 
140 

7;5 

5565 
787-5 
910 

posnofC.G. 

_  242  50 

W7ings 

56o 

7'5 

4200 

31545 

Fuselage  ... 

455 

iro 

5005 

=  7  '7°' 

Pilot 
Passenger.. 
Tail  unit  ... 

1  80 
)  80 
70 

8-0 
12-5 
28-0 

1440 
2250 
1960 

from  nose 
of  machine. 

Instruments 

35 

7-0 

245 

3I54-3 

24250 

Distance 

from 

Vertical. 

ground. 

Airscrew   ... 

87-5 

6-25 

547 

Engine 

600 

6-25 

3750 

Vert1  posn 

Fuel 

742 

4820 

of  C.G. 

Tanks 

105 

6'5 

683 

202  1  1 

Chassis 

140 

2'0 

280 

Wings       ... 

560 

7'5 

4200 

3154  5 

Fuselage  ... 

455 

6-25 

2845 

=  6-42' 

Pilot 

1  80 

675 

1215 

from 

Passenger... 
Tail  unit  ... 

1  80 

675 
6-0 

1215 
420 

ground  line 

Instruments 

35 

675 

236 

3I54-5 

202  1  1 

The  various  members  should  be  weighed  after  construction, 
and  the  C.G.'s  of  assembled  parts,  such  as  the  wings  and  fuselage, 
should  be  checked  experimentally  by  suspension.  The  table 
given  for  the  determination  of  the  C.G.  can  also  be  extended 
to  give  the  longitudinal  moment  of  inertia  of  the  machine,  and 
similar  tables  will  give  the  vertical  position  of  the  C.G.  and  also 
the  lateral  moment  of  inertia.  These  moments  of  inertia  are 
necessary  for  investigating  the  stability  of  the  machine. 


GENERAL    LAY-OUT   OF    MACHINES  415 

/ 

As  it  is  of  extreme  importance  that  the  calculated  position 
of  the  C.G.  should  agree  closely  with  its  actual  position  upon  the 
completed  machine,  it  is  necessary  that  the  true  position  of  the 
C.G.  of  the  machine  should  be  found  before  any  test  flight  takes 
place. 

All  fittings  to  spars  and  longerons  should  be  positively 
registered  in  place,  and  if  it  is  absolutely  necessary  to  pierce 
the  timber  to  effect  this,  the  cross-sectional  dimension  must  be 
suitably  increased  at  the  hole.  Similarly  any  local  strengthening 
of  steel  tubing  should  be  securely  fastened  in  position.  The 
radius  used  upon  all  plate  fittings  must  not  be  less  than  the 
thickness  of  the  metal  employed  in  such  fittings.  Whenever  it 
is  found  necessary  to  alter  the  angles  or  shapes  of  such  fittings 
during  erection,  they  must  always  be  re-annealed  after  altera- 
tion. The  keynote  of  the  lay-out  of  the  control  system  should 
be  simplicity  combined  with  accessibility.  Simplicity  in  the 
design  of  the  control  devices  leads  to  freedom  from  jamming, 
and  accessibility  ensures  that  the  system  receives  adequate 
attention  and  lubrication.  Complicated  inspection  doors  should 
be  avoided.  The  rudder  should  be  controlled  by  means  of  an 
adjustable  foot-bar,  provided  with  leather  heel  supports  ;  the 
elevator  should  be  actuated  by  means  of  a  column  moving  fore 
and  aft ;  and  the  ailerons  should  be  controlled  by  a  sideways 
movement  of  the  same  column  or  by  means  of  a  wheel  at  the 
top  of  the  column.  For  machines  weighing  over  5000  Ibs.  it  is 
advisable  to  use  balanced  ailerons,  rudders,  and  elevators.  The 
ailerons  should  be  interconnected,  and  ease  of  operation  of  the 
control  column  carefully  studied. 

As  part  of  the  fuselage  drawings  an  engine  installation 
drawing  should  be  prepared.  The  general  arrangement  will 
show  the  leading  features  of  the  scheme,  on  the  lines  suggested 
in  Chapter  VII.,  and  the  details  sheets  will  show  the  bearers, 
plates,  etc.  The  G.A.  drawing  might  with  advantage  also  show 
the  position  of  the  radiators,  tanks,  etc.  From  these  diagrams 
the  various  stresses  can  be  worked  out  as  required.  The 
mounting  of  the  engine  should  be  of  fireproof  construction,  and 
accessibility  to  the  various  parts  of  the  engine  requiring  atten- 
tion, such  as  magnetos,  carburettors,  pumps,  etc.,  should  be 
carefully  considered.  The  engine  controls  should  always  be 
operated  in  a  positive  manner  by  means  of  rods  or  similar 
mechanism.  Such  rods  should  not  exceed  three  feet  in  length 
unless  provided  with  suitable  guides  to  prevent  springing.  In 
order  to  keep  the  movements  of  the  controls  standardised  they 
should  conform  to  Air  Ministry  practice,  that  is,  the  throttle 
control  handle  moves  forward  to  open  the  throttle,  the  altitude 
control  handle  moves  forward  to  weaken  the  mixture,  the 


4i6  AEROPLANE    DESIGN 

magneto  control  handle  moves  forward  to  advance  the  ignition, 
and  the  petrol-cock  control  handle  moves  forward  for  the  '  ON  ' 
position.  The  corresponding  name  plates  should  be  marked 
SHUT— OPEN  ;  STRONG— WEAK  ;  RETARD— ADVANCE  ;  OFF— ON. 
The  method  of  coupling  up  the  various  controls  must  be  clearly 
marked  on  the  drawings. 

In  arranging  the  disposition  of  the  various  tanks,  care  must 
be  taken  to  see  that  petrol  will  be  fed  to  the  engine  in  any 
position  the  machine  may  assume  in  flight.  Where  several 
tanks  are  fitted,  each  should  be  separately  connected  to  ihe 
main  supply  pipe  to  the  carburettor.  In  these  feed-pipes  sharp 
corners  must  be  avoided,  or  air-locks  will  form  and  cut  off  the 
petrol  supply.  It  is  a  good  plan  to  run  them  behind  the 
longerons,  which  will  serve  as  a  protection.  The  clips  with 
which  they  are  attached  should  be  lined  with  felt  or  similar 
material.  The  tank  for  the  lubricant  should  be  of  sufficient  size 
to  hold  from  15%  to  25%  more  oil  than  is  actually  required  by 
the  engine  for  the  length  of  run  provided  by  the  petrol  tanks. 
Jt  is  a  good  plan  to  distinguish  the  oil  pipes  from  the  petrol 
pipes  by  using  clips  of  distinctive  colours,  and  the  filler  caps  of 
the  various  tanks  should  b^  of  ample  size  and  clearly  marked 
with  the  nature  of  the  contents. 

A  quantity  gauge  for  the  petrol  tanks  should  be  inserted,  also 
an  air-release  valve,  and  a  pressure  gauge  for  the  oil,  both  gauges 
being  placed  in  a  convenient  position  for  observation  by  the  pilot. 

Where  a  water-cooled  engine  is  employed,  a  detail  drawing 
should  be  prepared  showing  the  radiator  system,  and  reserve 
water  should  be  carried  at  the  rate  of  '25  gallons  per  100  h.p. 
per  hour  of  fuel  capacity.  Radiator  pipes  should  be  clipped  in 
the  same  manner  as  the  petrol  and  oil  pipes  by  a  clip  of  a  dis- 
tinctive colour,  blue  being  the  colour  usually  adopted. 

In  the  case  of  air-cooled  engines  the  efficiency  is  largely 
•dependent  upon  the  manner  in  which  the  cowling  is  arranged  to 
give  an  ample  supply  of  air  to  the  engine  and  oil  sump.  The 
•cowling  should  provide  protection  to  the  magnetos,  sparking 
plugs,  and  carburettors  from  rain,  while  still  allowing  easy  access 
to  these  units  by  means  of  doors  or  quickly  removable  pieces. 

The  engine  installation  diagram  should  indicate  the  manner 
in  which  the  exhaust  gases  are  carried  away  from  the  exhaust 
manifold,  and  care  must  be  taken  to  see  that  this  pipe  does 
not  approach  within  six  inches  of  any  woodwork  or  fabric. 
Riveting  is  preferable  to  welding  in  the  case  of  built-up 
exhaust  pipes. 

The  engine-makers  should  provide  an  earthing  switch  for 
each  magneto,  and  it  should  be  possible  to  earth  all  the 
magnetos  at  once  or  separately,  so  that  each  magneto  can  be 


GENERAL   LAY-OUT   OF   MACHINES 


tested  in  turn.  The  earthing  wires  should  not  be  jointed,  and 
the  main  earth  wire  from  the  switch  should  be  carried  direct  to 
the  engine.  All  wires  should  be  tested  after  installation,  and 
must  be  capable  of  easy  inspection. 

From  the  completed  general  arrangement  (Fig.  287)  it  is 
now  possible  to  estimate  the  resistance  of  each  item,  and  con- 
sequently the  total  resistance  of  the  complete  machine.  From 
these  particulars  the  centre  of  resistance  of  the  machine  can 
then  be  calculated.  The  resistance  of  each  separate  item  should 
be  estimated  as  carefully  as  possible,  taking  into  account  the 
slip-stream  and  interference  effects  wherever  possible.  Moments 
should  then  be  taken  about  a  fixed  datum  line  in  a  similar 
manner  to  the  balancing-up  process,  and  the  total  moment 
divided  by  the  sum  of  the  resistances  gives  the  line  of  action  of 
the  centre  of  resistance. 

Body  Resistance. — The  estimate  for  the  body  resistance  of 
the  machine  under  design  is  shown  in  Tables  LXV.  and  LXVI. 


TABLE  LXV. — BODY  RESISTANCE.     (OUTSIDE  SLIP  STREAM.) 


•if  ~-i 

!- 

ITEM. 

Size. 

Area. 

p7 

g» 

RxH 

REMARKS. 

» 

Sq.  ft. 

•I  . 

^  i  . 

&2& 

§& 

Inches. 

Vheels    

30  dia.  6  wide  x  2 

2-50 

IO'O 

1*25 

12*5 

Lxle        

30  x  2 

0-417 

0*625 

1*25 

0*78 

"ail  plane 

30x3 

0*625 

0*625 

575 

3-60 

nterplane  \  outer 

1*125  X72  X4 

2-25 

2*093 

775 

22-70 

struts      /inner 

1*75x72x4 

3-50 

4*55 

7*25 

33-00 

.ift  wires  — 

Front  outer    ... 

1  34  x  0*09  x  2 

0-168 

o'545 

775 

4-23 

Front  inner    ... 

72  x  0*14x2 

0*140 

0*455 

7-25 

3-30 

Rear  outer 

134  X  0*09  X  2 

0*168 

0*545 

7-50 

4-09 

Rear  inner 

72X0*11  X  2 

O'lIO 

0*358 

7*0 

2-50 

>own  wires  — 

Outer  F  and  R 

1  30  x  0*09  x  4 

0*325 

1-055 

7*75 

8-17 

Inner  F  and  R 

112x0*11x4 

0*342 

1*110 

7*25 

8*05 

/ing  struts 

36  X  I  X  2 

0-50 

2*50 

3'5 

875 

iileron  levers    ... 

8x|x4 

0-166 

0-415 

1  1*0 

4*56 

TOTAL 

— 

— 

25*72 

— 

116  23 

Centre  of  Resistance  of  Components  out  of  Slip  Stream  =  IL    2^  =  4*52'  from  datum. 


E  E 


4i8  AEROPLANE    DESIGN 

TABLE  LXVI. — BODY  RESISTANCE.     (!N  SLIP  STREAM.) 


0 

i 

> 

, 

8  |.a 

1  « 

ITEM. 

Size. 

Area. 

g~ 

RxH 

REMARKS. 

Sq.  ft. 

.£2  ctf  "o 

as  5  *~ 

06  £   O 

Ii§ 

Inches. 

Wheels   

0 

Q 





Axle         

54x2 

075 

1-125 

1-25 

1-41 

Front  struts 

(chassis) 

30  X  I'25  X2 

0-52I 

0-680 

2-75 

1-87 

Rear  struts 

3O  X  I  '25  X  2 

0*521 

0-680 

2-75 

l-87 

Bracing  lift 

Wires  front    ... 

42XO'I4X2 

6-082 

0-266 

7-25 

i'93 

Bracing  lift 

Wires  rear 
Body       
Tail  plane 
Tail-plane  levers 

42XO'II  X2 
II4X3 

0-064 

2-38 
0-I67 

0-208 
55lbs.* 
2-38 
0-418 

7-0 
6-25 

5'75 
5'75 

1-46 

344-00 
13-70 
2-40 

*  Deduced  from  expts, 
relating  to  Aeroplane 
bodies',  Chap.  VI. 

Tail  skid 

18x2 

0-25 

1-480!   3'5 

5-19 

Rudder  and  fin  ... 

36X3 

075 

0-750 

6-5 

4-88 

Central  wing 

Struts  front    ... 

36x  n  x  2 

0-55 

0-715 

8-75 

6-25 

Central  wing 

Struts  rear 

38  x  i  -o  x  2 

0-50 

0-65 

8-50 

5'53 

Central  wing 

bracing 

54  x  -09  x  2 

0-067 

0-216 

875 

1-91 

TOTAL      ... 

— 

— 

64-57 

— 

392-40 

Centre  of  Resistance  of  Components  in  Slip  Stream  =  — — —  =  6*08'  from  datum. 

64-57 

In  order  to  arrive  at  a  correct  estimate  of  the  resistance  it  is 
necessary  to  take  into  account  the  variation  of  the  resistance 
due  to  the  slip  stream  of  the  airscrew.  For  this  purpose  the 
curve  given  in  Fig.  174  may  be  used,  together  with  Formula  70. 
The  following  particulars  relating  to  the  airscrew  it  is  proposed 
to  use  are  also  necessary  for  the  evaluation  of  this  formula : 
Diameter  10  feet,  experimental  mean  pitch  lO'i  feet,  number  of 
blades  2,  revolutions  per  minute  1650,  k  =  4'6  X  io~7  Sub- 
stituting in  Formula  70,  Tractive  Power 

4-6  x  10     -  '  '     V 


'["0!  *,«,)'] 


si—     X    10' 

60 


960 


I  - 


GENERAL   LAY-OUT   OF   MACHINES  419 

From  this  relationship  the  values  given  in  Table  LXVII.  can  be 
calculated,  and  the  slip-stream  coefficient  determined  from 
Fig.  174. 

TABLE  LXVII. — CALCULATION  OF  SLIP-STREAM  COEFFICIENT. 
V  ft. /sec.  ...         60         80         100         120         140         160         180 

V2  ...         ...     3600     6400     10000     14400     19600     25600     32400 

V2/772oo  ...      -047      -083        -130        -187        -254        -332        -420 

i  -  (V2/772oo)...      -953      -917        -870        -813        746        -668        -580 
P  ...       915       880         835         780         715         640         556 

Tractive  power 

/IT—  — ^  9'X5       8-8         8'35         7'8         7'r5         6'4         T56 

(Airscrew  diameter)3 

Slip-stream  coeffct.     274       2*45       2*16         r88       1-65         1-5         1-37 

The  resistance  of  all  components  affected  by  the  slip  stream 
from  the  airscrew  must  be  multiplied  by  these  factors. 

From  Table  LXVI.  it  is  seen  that  the  estimated  resistance 
of  the  components  affected  by  the  slip  stream  is  64*57  Ibs.  at 
100  feet  per  second.  The  resistance  at  other  speeds 

=  -4_57_ x —   x  siip-stream  coefficient 
io4 

and  the  resistance  of  the  components  out  of  the  slip  stream 

2572  x  V2 
io4 

From  these  two  equations  the  body  resistance  of  the  machine  at 
various  speeds  can  be  calculated,  as  shown  in  Table  LVIII. 

TABLE  LVIII. — BODY  RESISTANCE  OF  MACHINE  AT 

DIFFERENT    SPEEDS. 

V  ft. /sec    ...         ...         ...     60       80       ioo       120      140      160      180 

Components  in  slip-stream     64     101        139       175      209      248      286 

Components  outside   slip- 
stream ...         ...         ...     9*2      16*5     257       37        50        66        83 

Total  resistance  RB         ...     73     117*5     l^5      212      259      314      369 

Wing|Resistance. — From  the  fundamental  equation 

W  =  Ky£A'V2 
8 


420  AEROPLANE    DESIGN 

the  necessary  lift  at  any  speed  can  be  obtained  by  putting  into 
the  form 

W 

PA'V2 
g 

350° 


•00237  x  500  x  V2 
2960 

-V2" 

and  when  Ky  has  been  determined,  the  corresponding  Kx  can  be 
read  directly  from  the  curve  of  aerodynamic  characteristics. 
Knowing  Kx,  the  drag  of  the  wings  Rw  can  be  determined  at 
each  speed,  and  by  adding  this  result  to  the  resistance  of  the 
body  the  total  resistance  of  the  machine  at  ground  level  can  be 
determined,  as  shown  'in  Table  LXIX. 

[TABLE  LXIX. — CALCULATION  OF  TOTAL  RESISTANCE. 

V             ...  ...        70          80        100        120        140        160  180 

Ky           ...  ...     '605     '461       '296       '205  'J51       'TI5  '  '091 

Kx     ...  ...  "051  '0294  '0137  '0127  '0118  '0118  "0127 

£(54o)KxV2=  Rw  320   241    175    234   296   387    527 

g 

RB  +  Rw  •••      393        358        340        446        555        7°i        896 


Horse-power. — The  horse-power  required  at  the  various  speeds 
is  obtained  by  the  use  of  the  formula 

.     ,       Resistance  x  Velocity 
Horse-power  required  =  

55° 

and  the  variation  in  engine  power  will  be  assumed  to  follow  the 
law  of  the  curve  shown  in  Fig.  277.  The  maximum  efficiency 
of  the  airscrew  will  be  taken  as  80%  at  a  forward  speed  of  1 20 
miles  per  hour.  The  rate  of  climb  in  feet  per  minute 

Horse-power  available  x  33000 
Weight  ot  machine 

Table  LXX.  can  now  be  prepared. 


GENERAL   LAY-OUT   OF    MACHINES  421 

TABLE  LXX.  —  HORSE-POWER  REQUIRED  AND  AVAILABLE,  AND 
RATE  OF  CLIMB. 

V  (ft.  per  second)  ...       70         80       100       120     140     160     180 

R  V 

-  =  H.P.  required     ...        50         52         62         97     141     204     293 

55° 
V/Vmax.    .........    -398      -455      -569      -682    795    -908      ro. 

Power  factor       ......  -56  '64  76  '86  '93  '98  ro 

320  x  -8  x  Fp    ......  143       164  195  220  238  251  256 

H.P.  available     ......  93       112  133  123  97  47  o 

Rate  of  climb  (ft.  per  min.)  876  1055  1250  1160  914  443  o 

The  effect  of  the  variation  of  the  slip  stream  will  be  to  alter 
the  position  of  the  centre  of  resistance  in  a  vertical  plane,  and 
it  is  therefore  necessary  to  determine  its  position  both  at  top 
speed  and  at  slow  speed.  These  positions  are  obtained  by 
combining  the  information  given  in  Tables  LXV.,  LXVI. 

Resistance  of  components  out  of  the  slip  stream 

at  a  speed  of  80  f.p.s.     =  2572  x     '64  =  i6'5  Ibs. 

at  a  speed  of  160  f.p  s.  =  2572  x  2*56  =  66*0  Ibs. 

acting  at  a  distance  of  4-52  feet  from  datum  line. 
Resistance  of  components  in  slip  stream 

at  a  speed  of  80  f.p.s.     =  64*57  x     '64  x  2^45  =  ioi€2  Ibs. 

at  a  speed  of  160  f.p.s.  =  64-57  x  2-56  x  1-5     =  248  Ibs. 

acting  at  a  distance  of  6-o8  feet  from  datum  line. 
Resistance  of  wings 

at  a  speed  of  80  f.p.s.     =  240  Ibs. 

at  a  speed  of  160  f.p.s.  =  400  Ibs. 

acting  at  675  feet  from  datum  line. 

Taking  moments  about  datum  line, 
For  a  speed  of  80  feet  per  second 

H'  -  74-5  +  615  +  1620   =  6.4 

357 
For  a  speed  of  160  feet  per  second 

,  _  298_+^o8  +  2700  = 


714 

so  that  there  is  a  variation  in  the  vertical  position  of  the  centre 
of  resistance  of  o%i6  feet  or  1*92  inches  over  the  speed  range. 

Knowledge  of  the  position  of  the  centre  of  resistance  enables 
the  final  balancing  up  of  the  machine  to  be  obtained  and  the 
direction  of  the  tail-loading  determined.  In  this  case  the  line 


422 


AEROPLANE    DESIGN 


of  pull  of  the  airscrew  acts  at  a  distance  of  6*25  feet  from  the 
datum,  so  that  the  resulting  thrust-resistance  couple  will  be  very 
small,  and  a  small  up  load  on  the  tail  will  correct  for  this  effect. 
The  tail-setting  for  various  flight  speeds  is  next  calculated  in 
the  manner  shown  in  Chapter  XI. 

The  various  performance  curves  for  the  machine  are  shown 
in  Fig.  288,  from  which  it  will  be  seen  that  the  estimated  flight 
speed  is  117  miles  per  hour,  as  against  120  miles  per  hour 
required  by  the  design.  It  will  be  noted,  however,  that  in  the 
calculation  of  the  resistance  and  the  available  horse-power,  no 
allowance  has  been  made  for  the  variation  due  to  the  change  in 


VetoaVy  (  .pa) 

FIG.  288. — Performance  Curves. 

the  density  of  the  atmosphere.  As  pointed  out  in  Chapter  I., 
these  two  items  will  have  a  neutralising  effect  upon  each  other, 
and  as  the  resistance  has,  if  anything,  been  over-estimated,  it  is 
extremely  probable  that  the  desired  performance  of  120  miles 
per  hour  at  10,000  feet  will  be  achieved  upon  the  trial  flights  of 
this  machine. 

In  order  to  reduce  the  labour  of  design  work  to  a  minimum, 
it  is  very  desirable  that  a  careful  record  should  be  kept  of  all 
machines  designed  and  built.  For  this  purpose  some  such  table 
as  that  shown  in  Fig.  289  should  be  prepared  and  rilled  in  as  the 
various  particulars  become  available.  Data  relating  to  some  of 
the  most  successful  machines  yet  built  is  given  in  Chapter  XIV., 
which  will  form  a  nucleus  upon  which  the  embryo  designer  can 
build  his  own  designs. 


ENGINE  :— 
Type 
B.H.P. 
No.  fitted 
Airscrew  r.p.m. 
Kngine  r.p.m. 
Fuel  p.  B.H.P. 
Oil  p.  B.H.P. 

Range 
Speed 
Ground 
10000ft. 
15000ft. 
Landing 
Climb 
to    5000ft. 
to  10000  ft. 
to  15000  ft. 
to  20000  ft. 
Ceiling 

R.P.M. 
Total  H.P. 

AEROPLANE 
Type 
No.  of  wings 

Span       Chord 
Top  wing 
Second 
middle 
Third 
Bottom 

Incid'ce  Dihedral 

Gap 

Stagger 

mis.       hrs. 
Time     Rate 

Overall  lenjrth 
Height 
Gap 
Chord 
Distance  from  L.E.  of  lower  wing  to  elevator  hinge 

Stability 
Longitudinal 
Lateral 

STRUCTURAL  UNIT 

AREAS 

WINGS 

Top  plane       
Second  plane...                 
Middle  plane       
Third  plane    
Bottom  plane          
Ailerons           
Struts  (No.  =        )  
External  bracing  wires  

WEIGHT  Ibs. 

Wt. 

Sq.  ft. 

%wt. 

TOTAL  WINGS    ... 

CONTROLS 

Tail  plane       
Elevator          
Fin         
Rudder  

TOTAL  CONTROLS    ... 

1 

Fusels 
Chassi 
Tail  si 
Contr< 

ige         

dd 

)ls          

TOTAL  BODY    ... 

TOTAL  WEIGHT  OF  STRUCTURAL  UNIT     

r  ' 

POWER  UNIT 

ENGINE 

Engin 
Airscr 
Radia 
Engin 

3  dry 

ew         
tor,  piping,  and  water    
3  accessories 

POWER  UNIT    ... 

W 
p 

Fuel  tanks  and  piping    
Oil  tanks  and  piping       
.  Fuel       
Oil 

TOTAL  WEIGHT  OF  POWER  UNIT         

USEFUL  LOAD 

Crew  ... 
Passengers  . 
Instruments 
W.T.      do. 
Luggage 
Cargo  ... 
Spares 
Sundries 

.        ... 

TOTAL  WEIGHT  OF  LOAD  UNIT  

TOTAL  WEIGHT 

OF  MACHINE       

FIG.    289. 


CHAPTER  XIV. 
THE  GENERAL  TREND  OF  AEROPLANE  DESIGN. 

*  Soon  shall  thy  arm,  unconquered  steam,  afar 
Drag  the  slow  barge,  or  draw  the  rapid  car  ; 
Or  on  wide  waving  wings  expanded  bear 
The  flying  chariot  through  the  field  of  air.' 

The  Botanic  Garden,  by  Erasmus  Darwin, 
published  1791. 

IT  seems  hardly  credible,  when  one  surveys  the  present 
science  of  aeronautics,  that  it  was  only  in  1903  that  the  Wright 
Brothers  were  making  their  first  experiments  in  aerodynamics 
and  their  flights  with  gliders  at  Kitty  Hawk.  A  brief  resume  of 
the  leading  facts  of  aeronautical  history  is  of  more  than  ordinary 
interest. 

In  1848  a  small  model  was  made  by  Stringfellow  which  flew 
for  about  forty  yards  under  its  own  steam,  but  it  was  not  really 
until  the  late  nineties  of  the  last  century  that  serious  attention 
was  devoted  to  the  problem  of  the  'heavier  than  air'  flying 
machine.  At  that  time  the  two  most  prominent  investigators 
in  this  new  field  of  science  were  Langley  in  America  and 
Hiram  Maxim  in  England.  Langley's  machine  had  a  wing- 
surface  area  of  70  square  feet,  a  steam  engine  of  one  horse- 
power weighing  7  Ibs.,  the  whole  arrangement  weighing  30  Ibs, 
It  was  designed  to  carry  no  passenger,  and  flew  under  its  own 
steam-power  upon  two  occasions  in  1896;  the  lengths  of  the 
flights  being  respectively  one-half  and  three-quarters  of  a  mile. 
Maxim's  machine  of  the  same  date  was  much  more  ambitious  in 
conception.  The  wing-surface  area  was  4000  square  feet,  the 
steam  engine  was  of  360  horse-power,  weighing  1200  pounds, 
and  the  whole  machine  weighed  8000  pounds.  It  was  designed 
to  carry  three  passengers,  and  on  its  trial  was  anchored  down  to 
rails  to  prevent  actual  flying.  The  check  rail,  however,  was 
torn  away  and  the  machine  wrecked  on  its  trial.  In  1897  Ader 
constructed  an  aeroplane  weighing  complete  iioo  pounds,  the 
power  unit  being  a  steam  engine  of  40  horse-power  and  weighing 
nearly  300  pounds.  This  engine  was  capable  of  pulling  the 
machine  along  the  ground  for  short  distances,  but  no  flight  was 
accomplished.  Meanwhile  Langley  was  still  experimenting  in 
America,  and  produced  in  1903  a  full-size  aeroplane  as  the 
result  of  his  researches.  With  his  power-driven  models  the 


FIG.   297. — The  Bristol  Monoplane. 


FIG.  298. — Bristol  Fighter  fitted  with  Wireless. 


To  foUo  w  page  424^ 


GENERAL  TREND  OF  AEROPLANE  DESIGN         425 

method  of  launching  from  the  top  of  a  house-boat  had  been 
adopted  with  successful  results,  but  when  applied  to  the  full- 
scale  machine  this  plan  proved  a  failure,  and  Langley  abandoned 
his  efforts  in  this  direction. 

Then  on  September  i/th,  1903,  the  Wright  Brothers,  after 
many  years  spent  in  experiments,  succeeded  in  flying  a  power- 
driven  machine  as  stated  in  Chapter  I.,  the  machine  weighing- 
750  pounds  and  being  equipped  with  a  16  horse-power  petrol 
motor.  This  first  flight  lasted  but  twelve  seconds.  Rapid 
progress  was  now  made,  and  in  1908  Wilbur  Wright  made  his 
sensational  flights  in  France,  and  although  he  was  at  first 
treated  as  a  *  bluffer,'  a  flight  lasting  for  over  ninety  minutes 
at  Le  Mans  in  the  September  of  that  year  dispelled  all  doubts 
about  actual  flight. 

Since  that  date  the  main  air  marks  to  record  are  the  crossing 
of  the  English  Channel  by  Bleriot  on  a  monoplane  in  July, 
1909 ;  the  great  development  and  expansion  of  aeronautics, 
owing  to  the  War,  from  1914-1918;  the  flight  of  a  ¥-1500 
Handley-Page  from  Ipswich  to  Karachi  (India)  by  stages  from 
December  I3th,  1918,10  January  i6th,  1919;  the  unsuccessful 
attempt  of  Hawker  and  Grieve  to  cross  the  Atlantic  on  a 
Sopwith  machine  on  May  I9th,  1919;  the  crossing  of  the 
Atlantic  on  June  I4th-i5th,  1919,  by  Alcock  and  Whitten- 
Brown  in  a  Vickers-Vimy-Rolls — from  St.  John's,  Newfound- 
land, to  Clifden,  Ireland,  a  distance  of  about  1900  miles,  in 
16  hours;  the  flight  of  Captain  Ross-Smith  and  three  com- 
panions from  Hounslow  (England)  to  Port  Darwin  in  Australia 
in  a  Vickers-Vimy-Rolls,  a  distance  of  11,300  miles,  between 
November  I2th  and  December  loth,  1919. 

Civil  aviation  opened  officially  in  England  on  May  1st,  1919. 
Table  LXXI.  shows  the  results  obtained  by  private  enterprise 
during  the  six  months  ending  October  3ist,  1919. 

TABLE  LXXI. — PROGRESS  OF  CIVIL  AVIATION  IN  ENGLAND, 
MAY  I5TH  TO  OCTOBER  3isT,   1919. 

Number  of  hours  flown         ...          ...          ...          ...  4,000 

Number  of  flights      ...          ...          ...          ...          ...  21,000 

Number  of  passengers          ...          ...          ...          ...  52,000 

Approximate  mileage            ...          ...          ...          ...  303,000 

Total  number  of  accidents  ...          ...          ...          ...  13 

Number  of  fatal  accidents 2 

It  will  thus  be  seen  that  more  than  25,000  passengers  were 
carried  for  every  one  fatally  injured,  so  that  flying  can  be  re- 
garded to  be  quite  as  safe  as  any  other  form  of  locomotion,  while 
offering  the  advantage  of  much  greater  speed. 


426  AEROPLANE    DESIGN 

The  Bleriot  Machine. — The  machine  used  by  Bleriot  in 
his  cross-Channel  journey  was  known  as  a  No.  XI.  type  mono- 
plane. The  fuselage  was  of  open  wooden  framework  braced  by 
steel  wires  throughout.  The  two  halves  of  the  main  plane  were 
set  at  a  slight  dihedral.  The  span  was  28*5  feet,  the  chord 
6'5  feet,  and  the  total  surface  area  151  square  feet. 

The  tail  plane  consisted  of  a  fixed  plane  at  the  rear  of  the 
fuselage  of  area  17  square  feet.  The  elevators  were  placed  on 
each  side  of  this  fixed  tail  plane,  their  total  area  being  16  square 
feet.  The  rudder  was  rectangular  in  form,  fixed  beyond  the  end 
of  the  fuselage,  and  having  an  area  of  4/5  square  feet.  Lateral 
stability  was  maintained  by  warping  the  main  planes,  as  in  the 
case  of  the  Wright  machines. 

The  power  plant  consisted  of  a  three-cylinder  25  h.p.  Anzani 
air-cooled  engine,  driving  a  two-bladed  airscrew  nearly  7  feet  in 
diameter  at  1350  r.p.m. 

The  total  weight  of  the  machine  was  about  700  Ibs.,  and  its 
maximum  speed  40  miles  per  hour. 


Reproduced  by  courtesy  of  'Flight.' 

FIG.  290. — Avro  Triplane,  1908. 

Avro  Machines. — One  of  the  pioneers  in  England  was 
A.  V.  Roe,  whose  early  experiments  in  aviation  have  led  to 
the  development  of  A.  V.  Roe  &  Co.,  Manchester  and  South- 
ampton. A  study  of  the  various  machines  produced  by 
this  firm  illustrates  the  progress  of  aeroplane  design  in  an 
interesting  manner. 

The  '  Bull's  Eye,1  as  the  triplane  with  which  Mr.  Roe  carried 
out  many  experiments  on  the  Lea  Marshes  in  1908-1909  was 
called,  weighed  only  200  Ibs.  It  had  a  surface  area  of  about 


GENERAL  TREND  OF  AEROPLANE  DESIGN        427 

300  square  feet,  while  the  engine  was  a  10  h.p.  Jap.  The 
fuselage  was  triangular  in  section,  the  pilot  being  situated  some 
distance  behind  the  main  planes.  The  main  planes  could  be 
swivelled  round  a  horizontal  axis  in  order  to  vary  the  angle 
of  incidence.  These  main  planes  could  also  be  warped  in  order 
to  maintain  lateral  stability,  while  directional  control  was  main- 
tained by  the  rudder  at  the  rear  of  the  tail  planes.  The  triplane 
tail  was  of  the  lifting  type,  and  was  rigidly  attached  to  the  rear 
end  of  the  fuselage.  Fig.  290  gives  a  very  good  idea  of  the 
general  appearance  of  this  machine. 

The  first  Avro  biplane  appeared  in  1911.  It  was  fitted  with 
a  35  h.p.  Green  engine,  only  the  nose  portion  of  the  fuselage 
being  covered  with  fabric,  while  the  body  was  triangular  in 
shape  as  in  the  triplane.  The  tail  plane  was  of  the  non-lifting 


Reproduced  by  courtesy  of  ''Flight' 

Fig.  291. — Avro  Biplane,  1911. 

type  fitted  with  elevators,  and  lateral  stability  was  obtained  by 
warping  the  main  planes.     (See  Fig.  291.) 

In  Fig.  2Q2A  is  shown  the  Avro  504  K,  which  is  a  modifica- 
tion of  the  Avro  1913  machine.  This  machine  has  been  used 
as  the  standard  training  machine  for  pilots  of  the  Royal  Air 
Force,  and  is  practically  the  only  early  machine  still  in  general 
use.  The  Avro  Spider  is  shown  in  Fig.  2926,  and  embodies  an 
entirely  different  type  of  wing-construction.  As  will  be  seen, 
the  struts  are  arranged  similarly  to  the  struts  in  the  Wireless 
Biplane  Truss  shown  in  Fig.  101,  and  the  side  elevation  is  of 
the  same  type  as  that  illustrated  in  Fig.  1 14  (the  Nieuport  'V'). 
Fig.  2920  depicts  the  Avro  Manchester  Mark  II.,  which  repre- 
sents the  probable  commercial  machine  of  this  firm.  It  is  a 
twin-engined  biplane,  and  follows  orthodox  construction  except 
that  the  ailerons  are  balanced  by  means  of  an  auxiliary  plane 
mounted  on  two  short  struts  from  the  main  aileron  and  placed 
slightly  ahead  of  it. 


428 


AEROPLANE    DESIGN 


© 


—  ARMADILLO  — 


r~^r~^ 

W 

—MANCHESTER    MAR*]!  — 


—  ARA  — 


Avro  Machines. 

FIG.  292. 


Armstrong-Whitworth  Machines. 

FIG.  294. 


FIG.  300. — 0-400  Handley  Page. 


Reproduced  by  courtesy  ot  Messrs.  Handley  Page,  Ltd. 

FIG.  301. — Front  and  Side  Views  of  ¥-1500  Handley  Page. 


GENERAL  TREND  OF  AEROPLANE  DESIGN        429 

In  order  to  illustrate  further  the  general  trend  of  aeroplane 
design,  the  most  interesting  machines  of  the  leading  aeronautical 
firms  of  Great  Britain  will  be  briefly  reviewed  so  far  as  par- 
ticulars are  available.  The  general  dimensions  of  the  machines 
dealt  with  are  summarised  in  Table  72,  and  their  performance 
and  weights  are  given  in  Table  73.  The  line  drawings  of  these 
machines  are  due  to  the  courtesy  of  Flight  and  have  all  been 
prepared  to  the  same  scale,  so  that  direct  comparison  is 
possible. 

Airco  Machines. — The  design  of  the  Airco  machines  has 
throughout  been  the  work  of  Capt.  G.  de  Havilland.  They 
were  on  this  account  formerly  termed  'de  H.  machines,'  and 
under  this  appellation  earned  a  well-deserved  reputation  during 
the  War.  The  first  of  these  machines  made  its  appearance  early 
in  1915,  and  was  a  two-seater  machine  of  the  pusher  type  fitted 
with  a  70  h.p.  Renault  engine.  It  was  followed  by  the  de  H.  I  A, 
practically  identical  in  dimensions  and  construction,  but  fitted 
with  a  120  h.p.  Beardmore  engine.  The  performance  of  this 
machine  was  quite  good  for  the  engine  power  available.  (See 
Fig.  293  A).  The  de  H.  4  machine  was  one  of  the  most  successful 
machines  produced  during  the  war,  and  was  used  for  all  pur- 
poses. It  is  a  tractor  biplane  of  ^ood  clean  design.  Various 
types  of  engine  have  been  fitted  to  this  machine,  the  first  being 
a  B.H.P.  200  h.p.  The  engine  power  has  been  gradually  in- 
creased until  at  the  present  time  some  of  these  machines  are 
fitted  with  450  h.p.  Napier  engines.  The  engines  most  fre- 
quently fitted  are  the  Rolls-Royce  250  h.p.  and  350  h.p.  types. 
(See  Fig.  293  B.)  Since  the  war  the  passenger  accommodation 
on  this  machine  has  been  enclosed  to  form  a  cabin  capable  of 
seating  two  persons,  and  in  this  form  the  de  H.  4  was  used  for 
many  journeys  between  London  and  Paris  in  connection  with 
the  Peace  negotiations.  An  Airco  4  R  (de  H.  4  fitted  with  the 
450  h.p.  Napier  'Lion')  won  the  the  Aerial  Derby  in  1919. 
The  de  H.  5  is  a  small  tractor  scout  in  which  the  chief  aim 
in  design  appears  to  have  been  the  provision  of  a  clear  field 
of  vision  for  the  pilot.  The  most  notable  constructional  feature 
of  this  machine  is  the  large  amount  of  negative  stagger,  and 
perhaps  it  was  due  to  this  fact  that  the  machine  was  not  easy 
to  handle.  (See  Fig.  293  c.)  The  de  H.  9  in  its  main  dimen- 
sions was  largely  av  copy  of  the  dfc  H.  4,  the  chief  difference 
being  in  the  fuselage.  The  pilot's  cockpit  is  placed  further  back, 
and  by  fitting  a  vertical  engine  the  front  portion  of  fuselage  has 
been  given  a  much  better  shape.  (See  Fig.  293  D.)  A  modified 
9,  fitted  with  Napier  '  Lion '  engine,  piloted  by  Capt.  Gather- 


43° 


AEROPLANE    DESIGN 


Scate     of      F««»- 


(ff         5          0'  10' 


SO'  40  50  60 


AtRCO     IQ* — 


FIG.  293. — Airco  Machines. 


GENERAL  TREND  OF  AEROPLANE  DESIGN         431 

good,  broke  eighteen  British  records  in  one  flight  on  Nov.  15th, 
1919.  This  machine  has  attained  a  speed  of  155  m.p.h.  The 
Airco  IOA  was  designed  for  long-distance  bombing  combined 
with  all-round  performance.  Table  LXXIII.  shows  how  well 
this  aim  was  achieved.  It  is  a  twin  -  engined  machine,  the 
Liberty  engines  being  placed  out  on  the  lower  wing  structure, 
one  on  each  side.  (See  Fig.  293  E.) 

Armstrong- Whitworth  Machines. — Since  the  A.W.  Quad- 
ruplane  is  the  only  example  of  this  type  of  machine  which  has 
been  constructed  by  British  aeronautical  engineers,  its  leading 
features  are  of  considerable  interest.  On  trial  it  was  found  that 
its  performance  was  slightly  inferior  to  that  of  contemporary 
triplanes  of  the  same  engine  power,  and  much  inferior  to  that 
of  small  biplanes.  The  load  per  brake  horse-power  is  somewhat 
high,  and  it  is  possible  that  the  fitting  of  a  more  highly  powered 
engine  would  lead  to  a  considerable  improvement  in  its  per- 
formance. (See  Fig.  294  A.)  The  Armadillo  is  noteworthy 
from  the  fact  that  the  fuselage  entirely  fills  the  centre  section 
of  the  wing  structure  (see  Fig.  294  B);  while  in  the  Ara  machine 
there  is  a  slight  gap  between  the  top  of  the  fuselage  and  the  top 
plane.  (See  Fig.  2940.)  Both  of  these  machines  are  single- 
seater  tractors,  and,  as  Table  LXXIII.  shows,  their  performance 
under  test  was  good. 

Bristol  Machines. — Although  the  monoplane  is  the  most 
efficient  type  of  aeroplane  aerodynamically,  it  fell  into  disrepute 
about  1912  on  account  of  several  fatal  accidents  which  occurred 
in  use,  owing  principally  to  structural  defects.  It  is  therefore 
very  creditable  that  Captain  Barnwell,  the  designer  of  the 
Bristol  machines,  has  produced,  in  the  face  of  much  opposition 
and  prejudice,  such  a  pleasing  and  efficient  monoplane  as  is 
shown  in  Figs.  296  A,  297  (p.  424).  As  will  be  seen,  the  wing 
section  employed  allows  of  deep  spars,  the  wing  being  fitted 
with  aileron  surfaces  instead  of  with  warping  arrangements  as  is 
usual  in  monoplane  practice.  Especial  care  has  been  devoted 
to  streamlining,  and  openings  are  provided  in  the  inner  portion 
of  the  wings  near  the  sides  of  the  fuselage,  resulting  in  a  further 
increase  in  the  natural  range  of  visibility  of  the  monoplane  type. 
The  Bristol  Fighter  (Figs.  296  B  and  298,  p.  424)  illustrates  a 
machine  designed  primarily  for  fighting  purposes.  The  F  2  B,  as 
it  was  also  called,  was  very  largely  used  for  fighting,  scouting, 
and  other  purposes  during  the  war,  and  the  illustrations  show  the 
modifications  that  have  been  made  in  the  design  of  the  fuselage 
and  other  components  in  order  to  render  this  machine  efficient 


432 


AEROPLANE    DESIGN 


© 


-—MONOPLANE-— 


— -FIGHTER— - 


FIG.  296. — Bristol  Machines. 


GENERAL  TREND  OF  AEROPLANE  DESIGN        433 

for  its  specific  purpose.  In  particular  it  will  be  observed  that 
the  lower  plane  is  situated  well  below  the  fuselage,  resulting  in 
a  somewhat  more  complicated  arrangement  of  the  chassis. 
Pilots  report  that  this  machine  is  very  responsive  to  its  controls, 
while  it  also  possesses  a  large  amount  of  inherent  stability. 
The  Bristol  Triplane  (Fig.  2960)  is  a  four-engined  machine 
driving  two  tractor  and  two  pusher  airscrews.  It  was  primarily 
designed  for  bombing  purposes,  but  is  being  adapted  for  other 
uses. 

Handley  Page  Machines. — From  the  very  inception  of  his 
firm  Mr.  Handley  Page  has  pinned  his  faith  to  the  future  of  the 
large  aeroplane.  The  first  Handley  Page  bombing  machines  did 
not  make  their  appearance  until  December,  1915,  and  it  was  not 
until  August  of  the  following  year  that  the  first  squadron  of  the 
O-4OO  type  was  formed  at  Dunkirk.  From  that  date  until  the 
conclusion  of  hostilities,  all  heavy  night  bombing  on  the  Western 
Front  was  performed  with  these  machines.  The  V-15OO  type 
was  designed  originally  to  bomb  Berlin,  but  is  now  being 
adapted  for  commercial  use.  One  of  these  machines  has 
carried  forty- one  passengers  to  a  height  of  8000  feet. 

A  line  diagram  of  the  O-4OO  type  is  shown  in  Fig.  299,  a 
front  view  of  the  O-4OO  in  Fig.  300,  while  front  and  side  views 
of  the  V-I5OO  type  are  shown  in  Fig.  301  (p.  424).  Photographs 
illustrating  the  position  of  the  wings  in  their  folded- back  position 
were  shown  in  Figs.  3,  151. 

Sopwith  Machines. — The  Sopwith  Tabloid  was  originally 
built  as  a  side-by-side  two-seater  for  Mr.  Hawker,  who  has  since 
achieved  fame  as  a  first-class  test  pilot,  and  whose  attempt  to  be 
the  first  airman  to  cross  the  Atlantic  on  a  Sopwith  machine  was 
only  frustrated  through  radiator  failure.  In  the  Tabloid  machine 
lateral  control  was  effected  by  means  of  wing-warping.  This 
machine  first  demonstrated  the  possibilities  of  the  small  single- 
seater  biplane  as  a  rival  to  the  monoplane  for  high-speed  work, 
while  retaining  a  large  range  of  flying  speeds.  (See  Fig.  302  A.) 
The  ij  Strutter  is  so  designated  because  of  the  type  of  wing- 
bracing  employed.  The  top  plane  was  in  two  halves  bolted  to 
the  top  of  a  central  cabane,  and  the  spars,  are  provided  with 
extra  support  in  the  shape  of  shorter  struts  running  obliquely 
from  the  top  longerons  to  the  top  plane  spars.  This  machine  is 
also  interesting  owing  to  the  fact  that  it  was  fitted  with  an  air 
brake  taking  the  form  of  adjustable  flaps  inserted  into  the  trailing 
edge  of  the  lower  plane  close  to  the  fuselage.  Another  feature 
incorporated  in  the  ij  Strutter  was  the  tail-plane  variable  incidence 

s   F  F 


434 


AEROPLANE   DESIGN 


gear.  (See  Fig.  302  B.)  The  Sopwith  Pup  follows  the  general 
lines  of  the  ij  Strutter  and  the  original  Tabloid.  It  handles 
remarkably  well,  and,  as  will  be  seen  from  Table  LXXIIL, 


—  O-  4OO  — 


o 


FIG.  299. — Handley  Page,  0-400. 

possesses  a  very  low  landing  speed.  (See  Fig.  3020.)  The 
Sopwith  Camel  was  so  called  from  the  hump  which  it  possesses 
on  the  forward  top  side  of  its  fuselage,  due  to  the  fitting  of  two 


GENERAL  TREND  OF  AEROPLANE  DESIGN        435 


_J_5 


53 J 

T^ 


© 


HC 


Scale     of 


)flf          5'          O'  10'  20' 


XT 


© 


FB 


— -TRi  PLANE.  — 


FIG.  302. — Sopwith  Machines. 


436  AEROPLANE    DESIGN 

fixed  machine  guns  both  firing  through  the  airscrew.  It  achieved 
a  great  reputation  during  the  War,  but  as  a  sporting  machine 
the  Pup  is  preferable  in  many  respects.  (See  Fig.  302!).)  The 
Dolphin  (see  Fig.  302  E)  differs  considerably  from  the  Camel  in 
structural  arrangements.  It  will  be  seen  in  the  illustration  that 
a  double  bay  arrangement  of  struts  has  been  adopted,  the  gap 
has  been  diminished,  and  negative  stagger  introduced.  The 
radiator  was  divided  into  two  portions,  placed  one  on  either  side 
of  the  fuselage  opposite  the  pilot's  cockpit,  each  radiator  being 
fitted  with  deflectors.  The  Sopwith  Triplane  was  designed 
solely  to  afford  good  visibility  and  manoeuvrability.  As  will  be 
seen  from  the  figures  and  tables,  the  wing  chord  has  been 
considerably  reduced,  and  single  '  I '  struts  have  been  fitted 
between  the  planes  in  place  of  the  more  usual  pair. 

Vickers  Machines. — At  the  commencement  of  the  war  the 
Vickers  Gun  Bus  (F.B.  5)  (Fig.  303 A)  was  practically  the  only 
fighting  aeroplane  in  existence.  It  was  a  pusher  machine,  the 
Vickers  gun  being  mounted  in  the  nose  of  the  nacelle,  from 
which  position  a  very  wide  range  of  unobstructed  fire  could  be 
obtained  ;  and  its  arrival  on  the  Western  Front  established  for 
the  time  being  the  aerial  supremacy  of  the  Allies.  The  F.B.  7 
(Fig.  3036)  was  brought  out  in  August,  1915,  and  was  one  of 
the  first  twin-engined  machines  to  take  the  air.  It  is  par- 
ticularly interesting  as  being  the  prototype  of  the  now  famous 
'Vimy  Bomber.'  In  the  experimental  model  of  the  F.B.  16 
trouble  developed  owing  to  the  weakness  of  the  leading  edge 
of  the  main  planes.  Investigation  showed  that  this  weakness 
resulted  from  an  inadequate  factor  of  safety  for  the  high  speed 
attained  by  this  machine.  After  remedying  this  defect,  the 
machine  was  tested  officially  and  showed  a  performance  better 
than  that  obtained  by  contemporary  machines  of  a  similar  type. 
The  Vimy  Bomber  (Figs.  30313,  304,  p.  432)  was  remarkable  for 
its  small  size  when  compared  with  its  large  lifting  capacity.  It  is 
claimed  that  this  machine  is  stable  both  longitudinally  and 
laterally.  The  engines  are  placed  out  on  the  wing  structure 
directly  over  the  landing  chassis.  The  fore  part  of  the  fuselage 
is  constructed  of  metal  tube  and  the  rear  part  of  special  wooden 
tube.  This  machine,  as  used  for  crossing  the  Atlantic,  is  shown 
in  the  Frontispiece  and  Fig.  304,  and  it  is  noteworthy  that  with 
the  fitting  of  additional  fuel  tanks  only,  it  succeeded  in  accom- 
plishing the  first  direct  flight  across  the  Atlantic.  An  exactly 
similar  type  machine  accomplished  the  first  flight  to  Australia. 
Fig.  305  (p.  432)  shows  the  Vimy  as  adapted  for  commercial  work. 
Details  of  this  machine  have  already  been  given  in  Chapter  VII. 


GENERAL  TREND  OF  AEROPLANE  DESIGN        437 

Boulton  and  Paul  Machines. — Illustrations  of  two  of  the 
machines  manufactured  by  this  firm  are  shown  in  Figs.  306,  307 
(p.  444).  It  will  be  noticed  from  Table  LXXIII.  that  the  load 


© 


—  r.6-5  — 


V     —  F.B.   7  — 


Scale       of       P*e^ 


'050  10  20  SO 


40  50  fcO  70 


© 


F.B.  f6  — 


FIG.  303. — Vickers'  Machines. 


per  horse-power  for  the  passenger  machine  is  only  7-8  Ibs., 
which,  coupled  with  particular  care  in  the  remainder  of  the 
design,  in  a  large  measure  accounts  for  the  remarkable  per- 
formance of  this  type. 


4,3 


AEROPLANE    DESIGN 
TABLE  LXXII. 


TYPE 

WING  SPAN. 

WING  CHORD. 

WING  AREA. 

OF 

Over- 

all 

MACHINE. 

length 

Top. 

Middle. 

Bottom. 

Top. 

Middle   Bottom      Top.      Middle    Bottom 

Total. 

AVRO 

feet 

feet 

feet 

feet          feet 

feet          feet 

sq  .  feet    sq  . 

feet    sq.  feet 

sq.  feet 

504  K     
Spider     ... 

28-92 
2O  "5 

36-0 

28-5 

— 

36-0        4-83        —          4-83       171-5        - 

21-5    i  6-00  1               2-5       162-0 

-        I58-5 
—    -j    46*0 

330-0 

208-0 

ManchesterMk.il 

60  -o 

— 

60*0       7-5   '    —        7-5       430-0 

-        387-0 

817*0 

AIRCO 

IA           

29-0 

41*0 

— 

41-0 

5'9 

—          5-9         187-0 

-        175-25 

362-25 

4           

30-0 

42*39 

— 

42*39 

5'5 

—          5-5         223-0        - 

-         211-0 

434-0 

5          

22-0 

25-67 

— 

25-67 

4'5 

—          4-5          lll'2 

—       100-9 

2I2-I 

9          

30-83 

42-39 

— 

42-39 

5'5 

5'5       223-0      - 

2II*O 

434-0 

IOA           

39-62 

65-5 

— 

65-5 

7-0 

—        7-0 

429-2        - 

408-2 

837-4 

A-WHITWO 

RT 

H 

(2)27-83 

(2)3'58 

(2)92-6 

Quadruplane     ... 
Armadillo 

22-25 
18-83 

27-83 
2775 

27-83 

2775 

3]58 

(3)3-58    3*58 
~~        4'5 

102-6  (3)92-6,  102-6 

I2t-,'0                    "I25-0 

398-4 
250*0 

Ara        

20-25 

27-42 

— 

27-42 

5-25 

4'5 

147-0        - 

-       IIIO'O 

257-0 

BRISTOL 

Monoplane 

20-33 

3075 

— 

— 

5-92 

—    i     — 

145.0        - 

—             

145-0 

Fighter... 
Triplane 

2575 

81-67 

8l-67 

39'25 
78-25 

8-5 

*~s    I-! 

202-5        —        202-5 
650*0    650-0     605-0 

405-0 
I905-0 

HANDLEY 

PA 

GE 

0-400    

62-85 

I  OO'O 

— 

70  -o 

10-0 

—         IO'O 

1020-0  i      - 

-         625*0 

1645-0 

SOPWITH 

Tabloid  

20-33 

25*5 

—         25-5 

5-12 

5*12     128*3  j 

-       <  "3"0 

241-3 

l£  Strutter 

25*33 

33-5 

33'  5 

5'5 

—       5*5       183-0      - 

—         I7O-O 

353*0 

Pup        

19-33 

26-5 

-       26-5 

5-12      —        5-12      132-0 

122-0 

254-0 

Camel    ... 

1875 

28-0 

28-0      4-5        —        4-5       125-0 

II5.O 

240-0 

Dolphin 

22-25 

32-5 

—       32-5       4'5    i               4'5       i32>0      - 

—         I3I-O 

263-0 

Triplane 

18-83 

26-5 

26-5     ^26-5       3-25     3'25      3'25 

84-0       72-0    i     75-0 

231*0 

VICKERS 

F.B.  5  

27-17 

36-5                  36-5      5*5       —       5*5 

I97-0        - 

185-0 

382-0 

F.B.  7  

36-0 

1  181-0 

640*0 

F.B.  16  

25-0                  22-33     5'5                  4-i7  !  126-0 

81-0 

2O7-O 

vi™y     i  43*54 

67-17 

—       67-17   10-5        —      10-5       686-0 

644-0 

I330-0 

BOULTDN  &    PA 

UL 

:                ; 

Scout     

20-0 

29-0 

29-0    !  5'37                 4'i2     152-0      - 

—      114-0 

266-0 

Passenger 

40*0 

59  'o 

—       59-0       8-0        —        6-5 

432-0        - 

-      ;  338-0 

770-0 

S.E.  5       

20*92 

26-62 

—       26-62  i  5-0       --    |    5-0 

130-0        - 

-  ;  113'° 

249-0 

I 

i 

GENERAL  TREND  OF  AEROPLANE  DESIGN       439 


TABLE  LXXII. 


INCIDENCE. 

Gap. 

Stagger 

DIHEDRAL. 

AREA  OF  CONTROL  SURFACES. 

Top      Middle.  Bottom. 

Top. 

Middle/Bottom 

Tail 

Aileron  plane. 

Elevator 

Total.     Fin. 

Rudder 

Total. 

feet 

feet 

1  sq.  ft.     sq.  ft. 

sq.  ft. 

sq.  ft.    sq.  ft. 

sq.  ft. 

sq.  ft. 

4-5°       - 

4-5°  !  5-5 

2-17 

2'5° 

--      2-5° 

45'5      26-0 

18-0 

44-0  !    — 

90 

9-0 

O'O°          — 

O'O°         4'22        2'OO 

0-0° 

—      0-0° 

22-0      I5-2       10-4 

25-6      - 

7'8       7-8 

4-0° 

4-0°      7-25      o-o 

2-5° 

—     2-5°  * 

124-0     50  -o     35-0 

85-0    12-0    16-0     28-0 

j 

5-5°     — 

5-5° 

5-87      o-o 

3-0° 

3-o° 

64-0 

37  '5 

23-0 

60-5 

i 
37    '5'4    s  19-1 

3-0°      5  -50;     i-o     3-0° 

—      3-0° 

82-0      38*0      24-0 

62-0 

5'4 

13-7      19-1 

2'O°          —          2'O° 

475-2-25    4-5° 

4'5° 

46-4       13*4       12-2 

25  6        2-2 

6-3 

8  '5 

3-0°                        3-0° 

5-50      i-o     3-0 

—       3'o° 

82-0 

38-0 

24-0 

62  0  ;     5'4 

137 

19-1 

7-0°       -       7-0° 

7-0 

O'O 

4'5° 

-      4'5° 

118-0     75"5 

33'* 

1086 

IO'O 

2575 

3575 

(2)  3'°° 

(2)  i'5° 

3'o°   (3)  3  °°   3'°° 

2-67      1-42    i  -5° 

(3)  i-S°  i  5° 

67-2 

— 

16  o 

16-0      i  '9 

8-0 

9'9 

2-25°     -       1-0° 

3-92      0-71    0-0° 

—         2'0° 

36-0 

17  o 

14-0 

31-0      1-6 

6-0 

7-6 

2-75°     —       1-25° 

3-88    0-96^-5° 

—      ,1-5° 

20'4 

25-0 

24-0 

490 

2-5 

iro 

I3-5 

O'O°          — 

_ 

—      —   i  2-0° 

18-0 

20  -o 

15-0 

35-o 

5-0 

4'5 

9  "5 

i  '5°       —       1*5" 

5-42      1-42    3  -5°       —      3  -5° 

5°'° 

22*2 

23-2 

454 

107 

7-2      17-9 

2'5°      2-5°     2-5° 

7-21      —      2-0° 

2-0°       2-0° 

192-0 

96-5 

85-0 

181-5 

28-2 

25-0 

51-2 

—        —         — 

I  I'O 

— 

4-0° 

4'0° 

— 

I23-5 

65-3 

1888 

14-7 

45'7 

60-4 

i-oc                 1-0°    1  4-5       0-92    i  -5° 

•  *'5° 

28-0     1  1  -8 

n-8 

23-6      r8 

41-3 

6-r 

2-45                 2-45° 
i-5°  I               i'5° 

4-42 

2-0 

I'5 

?/ 

~      I'4/ 

52-0     35-5     21-5 

22-0       23-0,     1  1  -8 

570     3'5 
34-8      3'5 

7-25 

4'5 

1075 
8-0 

2-0°                 2-0°      5-4 

1-5     0.0° 

5'°° 

36-0     14-0;    10-5 

24-5  !    3'° 

49 

7'9 

2-oJ                  2-0°    ;  4-25 

-  I'O- 

2'5° 

—      2-5° 

38-0    17-0    13-5 

30-5      3'5 

80 

2'O°         2'O°       2'O° 

3-0 

J'5 

2-5° 

2'5°     2-5° 

34-0     14-0      9-6 

236      2-5 

4'5 

7-0 

4'5°                 4'5°       6-0 

O'O        I'O° 

—       1-0° 

57-0    560    24-6 

80-6 

8-5 

13-25 

2175 

3-0°      —      3-0°     7-33     0-92  3-0° 

—       3-0° 

93  o     42-0     28-5 

705 

20  -o 

20-0 

2-0°          —          2-0°         3-92        2'5     j   I'5° 

—       1  '5° 

23-5     18-5     15-3 

33-8 

6-5 

6-0 

I2'5 

3'5°          — 

3-5°     io-o       o-o     3-0° 

30° 

242-0  !  1  14-5 

630 

177-5 

2X 

2X 

48-5 

1 

! 

... 
i 

1 

! 

5-o°       - 

5-o° 

4-6        1-5     5-0° 

5-0° 

I 
30-2  !  -5-1 

15-1 

30*2 

6-5 

6-0 

12-5 

1 

j                                 I 

i 

440 


AEROPLANE   DESIGN 
TABLE  LXXIII. 


TYPE 
OF 

ENGINE, 

WEIGHT 
OF  MACHINE. 

Fuel 
capacity.      Range. 

MACHINE. 

Name. 

No. 

H.P. 

Empty. 

Loaded. 

Hours. 

-Miles. 

L1JS. 

J.bs. 

AVRO 

504  K      

Le  Rhone 

I 

no 

1230 

1820 

3-0 

225 

Spider     
Manchester  Mk.  II.     ... 

Clerget  
Siddeley 

I 
2 

I3° 
600 

963 
4580 

1517 
7160 

3-0 

3'8 

330 

450 

AIRCO 

I  A          

Beardmore 

I 

1  2O 

— 

2400 

— 

— 

4            

Rolls-Royce 

I 

370 

— 

3340 

4-0 

500 

5           

Le  Rhone 

I 

1  10 

— 

1490 

2'0 

200 

9           

Lion  (Napier)  .. 

I 

420 

— 

3725 

— 

— 

IOA            

Liberty  ...         ... 

2 

800      ! 

8500 

5'° 

650 

A-WHITWORTH 

Quadru  plane 

Clerget  ... 

I 

I3O 

1140 

I800 

— 

— 

Armadillo 

B.R.  2  ... 

I 

230             1250 

1860 

275 

— 

Ara          

Dragonfly 

I 

320 

1320 

1930 

3-25 

450 

BRISTOL 

Monoplane 

Le  Rhone 

I 

1  10 

1300 

—            — 

Fighter  
Triplane... 

Rolls-Royce 
Siddeley 

I 

4 

250      j 

1000         9300 

2800 
16200 

; 

— 

HANDLEY    PAG 

E 

0-400     

Rolls  Royce 

2 

700         ;         8000 

14000 

7-0 

650 

SOPWITH 

Tabloid  

Gnome  

80                     730 

I  120 

3*5 

320 

i£  Strutter 

Le  Rhone 

1  10         1280 

22OO 

Pup         

Gnome  ... 

loo           856 

1297 

2'O 

2OO 

Camel     

B.R.  i  

J50 

1470 

2-6 

3«o 

Dolphin  ... 
Triplane  

Hispano  Suiza  ... 
Clerget  

I 

200 
130 

1406 
1  100 

1880 
1540 

2'O 

230 

310 

VICKERS 

F.B.  5    

Gnome  ... 

I 

100             1220 

2O5O 

4'5               330 

F.B.  7    

Gnome  ... 

2 

200            2130 

3200 

2'5               200 

F.B.  16  

Hispano  Suiza  ... 

I 

200             1380 

1880 

2-25 

300 

Vimy 

:  Rolls-Royce      ... 

2 

700 

6700 

12500 

1  I'OO 

IIOO 

BOULTON  &  PA 

UL 

Scout      

B.R.  2  

I 

230 

1230 

I92O 

3-5 

440 

Passenger 

Napier  Lion 

2 

900 

4OOO            7OOO 

3-0 

— 

S.E.5        

Hispano  Suiza  .. 

I 

200 

— 

1980 

2 

250 

GENERAL  TREND  OF  AEROPLANE  DESIGN 
TABLE  LXXIII. 


44 1 


SPEED. 

CLIMB. 

Ceiling. 
Feet. 

Landing 
speed. 

m.p.h. 

LOAD. 

(  1  round 
level. 

At 

1  0000  ft. 

At 
15000  ft. 

Minutes  to  — 

Per  sq.ft.    PerH.P. 

5000  ft. 

10000  ft.       15000  ft. 

90                 75 

65 

6-25 

l6'0 

40-0 

— 

35 

5'52    !      16-5 

1  20          no 

4-0 

9*5           22*0 

19000 

40 

778    i      1  1  "6 

125           119 

112 

1  1  '15         40*0 

17000 

45 

876     |       11-9 

* 

. 

89            - 

— 

IO'O 



6-6 

20'0 

133 

J26 

— 

9-o           16-6 

23500 

52 

7'4 

9*4 

1  02 

89 

— 

12-4           27-4 

17000 

50 

7-0 

13-6 

140 

135 

— 

8.2 

14-6 

25300 

8'5 

8-8 

124 

117 

" 

II'O 

20-5 

20000 

55 

10  '0 

io'6 

105 

99 





17-0 

25000 

4-5 

'3*9 

125           113 

— 

— 

6'5 

— 

24000 

55 

7  '4 

8-0 

150 

145 

4'5 

— 

28000 

£5 

7  '5 

6-0 

130 

117 

_ 

3-5 

9-0 

19-0 

_ 

49 

8-97 

10-8 

125 

"3 

— 

irs 

21-5 

— 

48 

6-92 

1  1  '2 

1  06            93 

35-0 

— 

55 

8-5 

16-2 

— 

85 

< 

— 

— 

— 

— 

8-5 

20  go 

92 



_ 

36 

4.66 

14-0 

— 

103 

8-0 

18-9       41-5 

l6000 

35 

6-4 

17-5 

1  IO 

104 

100 

57 

12-4           23-4 

18500 

30 

5*2 

12-4 

— 

120 

114 

— 

8-3           15-8 

23000 

35 

— 

128 

124 

3  '9 

8-25 

147 

23500 

40 

7*3            9'0 

106 

95 

5*0 

11-8 

22-3 

21000 

35 

6-0           12-4 

75 



_ 

16-0 

9000 

4i 

5*4          20-5 

So 

— 

— 

18-0 

—            — 

I2OOO 

40 

5*0          16-0 

— 

135 

126 

475 

10-4          2075 

20000 

55 

9-1            9-4 

105 

100 

15-0 

50-0 

10500      ! 

5° 

9*4           17*9 

.  , 

125 

no  ' 



9'5 

18-0 

21000 

50 

7-2             8-3 

149 

142 

~ 

8-0 

15-0 

25OOO 

54 

9-1             7-8 

— 

— 

120 

5-o 

10-8 

20-8 

21000 

8.0            9-8 

j 

. 

442  AEROPLANE    DESIGN 

Official  Machines. — Probably  more  controversy  has  raged 
round  the  B.E.  2  C  than  any  other  aeroplane  built,  nevertheless 
it  represents  the  type  of  aeroplane  that  will  undoubtedly  be 
largely  developed  in  the  near  future,  namely,  the  inherently 
stable  machine.  Its  inception  and  development  was  principally 
due  to  the  efforts  of  the  late  Mr.  E.  T.  Busk,  of  the  Royal 
Aircraft  Factory,  and  it  shows  in  a  striking  manner  the  result 
of  a  sound  application  of  theory  to  practice.  Table  I.  illustrates 
how  near  the  actual  performance  of  this  machine  approached 
the  calculated  values.  The  S.E.  5  represents  the  most  successful 
war  product  of  the  R.A.E.  In  general  appearance  it  is  similar 
to  the  Sopwith  ij  Strutter,  and  was  designed  as  a  single- 
seater  fighting  machine.  It  is  inherently  stable,  a  wonderful 
demonstration  of  its  qualities  in  this  direction  being  provided 
when  a  S.E.  5  machine  returned  safely  to  the  British  lines  after 
its  controls  had  been  practically  shot  away  over  the  German 
lines. 

Having  considered  the  general  trend  of  design  with  reference 
to  complete  machines,  there  only  remains  to  be  considered  the 
question  of  detail  design. 

CHOICE  OF  TYPE. — It  would  be  rash  to  prophesy  whether 
the  monoplane,  biplane,  or  multiplane  will  be  the  most  largely 
developed  type  in  the  future,  since  each  type  possesses  advan- 
tages peculiar  to  itself.  In  comparison  with  the  biplane,  the 
monoplane  can  carry  5  per  cent,  more  weight  per  square  foot 
of  wing  surface,  besides  giving  much  better  visibility.  On  the 
other  hand,  it  is  much  weaker  structurally.  In  the  same  way 
the  triplane  and  quadruplane  are  about  5  per  cent,  less  efficient 
than  the  biplane  and  triplane  respectively,  but  if  well  designed 
should  be  more  manoeuvrable. 

Generally  speaking,  it  seems  probable  that  the  biplane  will 
hold  its  own  for  general  purposes  for  some  considerable  time  to 
come,  with  the  triplane  as  a  rival  in  the  larger  sizes. 

Wing  Design. — The  wind  channel  method  of  investigation 
has  produced  very  efficient  forms  of  aerofoils,  and  it  seems  pro- 
bable that  seventeen  is  an  optimum  value  of  the  Lift/Drag  ratio 
for  wings  of  practical  design.  Further  investigation  is  needed 
as  to  the  depth  of  camber  and  the  nature  of  the  flow  in  the 
neighbourhood  of  the  aileron  surfaces.  It  is  probable  that  in 
the  near  future  metal  construction  will  replace  wood  for  the 
ribs  and  spars  of  large  machines  at  least. 

Optical  stress  analysis  has  shown  that  there  is  considerable 
divergence  between  the  points  of  inflexion  as  calculated  from 


5  y 


51 
I 

^> 

I 

I 

* 

1 


GENERAL  TREND  OF  AEROPLANE  DESIGN        443 

the  Theorem  of  Three  Moments  and  the  points  obtained  by 
loading  a  spar  approximately  as  in  practice,  and  further  inquiry 
into  this  discrepancy  is  required.  It  seems  at  least  on  the  safe 
side  to  use  the  Theory  of  Bending  as  outlined  in  Chapter  V. 

For  large  machines  the  saving  in  weight  obtained  by  using 
tapered  struts  is  of  great  importance,  and  it  is  hoped  that  the 
graphical  method  of  tackling  their  design,  which  has  been  fully 
explained  in  Chapter  V.,  will  enable  all  those  whose  knowledge 
of  the  Calculus  is  limited,  or  even  non-existent,  to  apply  this 
theory  in  practice. 

Internal  bracing  is  generally  effected  by  either  plain  or 
stranded  wire  in  machines  of  all  countries,  the  Fokker  biplane 
and  triplane  being  notable  exceptions.  A  great  improvement 
in  the  design  of  the  wings  will  be  the  development  of  a  section 
with  a  stationary  centre  of  pressure  over  the  range  of  flying 
angles.  Further  improvements  likely  to  follow  are  : 

(i)  A  practical  design  for  a  variable  camber  of  surface,  in 
which  the  mechanism  is  simple  and  reliable,  and  does 
not  add  appreciably  to  the  weight  of  the  machine. 

(ii)  The  elimination  of  the  major  portion   of  the  external 
bracing  of  the  wing  structure. 

Fuselages — The  design  of  the  fuselage  is  largely  governed 
by  the  type  of  engine  employed  and  the  particular  purpose  for 
which  the  machine  is  intended.  Recent  investigations  tend  to 
show  that  the  circular  (or  elliptical)  body  does  not  possess  any 
material  advantage  over  the  square  section.  Constructionally,, 
either  wooden  formers,  suitably  lightened  out  and  of  the  required 
cross-sectional  shape,  support  the  longerons  at  regular  intervals ; 
or  the  strut  and  cross-bracing  wire  method  is  used.  It  may  be 
remarked  in  passing  that  enclosing  the  rear  portion  of  the  body 
of  several  well-known  war  machines  has  led  to  a  reduced  overall 
resistance  and  consequent  improvement  in  performance. 

The  monocoque  method  of  fuselage  construction,  which  dis- 
penses with  the  longerons  and  employs  a  moulded  three-ply 
method  of  construction,  offers  considerable  advantages  from  the 
commercial  point  of  view,  since  internal  bracing  is  not  needed,, 
and  consequently  the  space  inside  the  fuselage  is  left  clear  for 
passengers,  luggage,  and  cargo. 

Control  Surfaces — As  shown  in  Chapter  XL,  the  attain- 
ment of  stability  by  means  of  a  correct  disposition  of  the 
various  control  surfaces  in  relation  to  the  fixed  surface  areas  of 
the  machine  itself  is  now  well  within  the  compass  of  the  aero- 


444  AEROPLANE    DESIGN 

plane  designer.  It  is  also  possible  to  achieve  stability  by  means 
of  external  stabilising  devices,  such  as,  for  example,  the  use  of 
-a  gyroscope,  but  the  success  of  the  inherently  stable  machine 
has  obviated  the  need  for  developing  such  methods. 

The  Airscrew. — Rapid  development  has  taken  place  in  the 
design  of  the  airscrew  during  the  war  period,  and  it  is  now  stated 
that  the  limit  to  the  speed  of  the  airscrew  is  fixed  by  the  circum- 
ferential velocity  of  the  tip,  which  must  not  exceed  the  velocity 
of  sound  (iioo  feet  per  second).  Airscrews  must  therefore  be 
geared  down  so  that  the  maximum  tip  speed  under  no  circum- 
stances is  greater  than  1000  feet  per  second.  Metal  airscrews 
have  been  manufactured,  and  will  probably  be  developed  for 
countries  where  the  climatic  conditions  do  not  permit  of  a 
continued  use  of  a  wooden  airscrew.  There  are  also  several 
experimental  designs  of  airscrews  with  variable  pitch  under 
trial,  of  which  more  will  doubtless  be  heard  in  the  future. 

Performance. — With  the  passing  of  the  special  conditions 
imposed  by  the  War,  the  need  for  very  rapid  climb  will  dis- 
appear, and  aeroplanes  will  cease  to  be  required  to  operate  at 
20,000  feet,  and  to  be  capable  of  reaching  that  height  in  the 
minimum  time. 

The  engine  employed  is  a  vital  factor  in  the  performance  of 
any  machine,  and  it  is  quite -a  truism  that  in  all  far-reaching 
•developments  the  aeroplane  designer  has  to  wait  upon  the 
engine  designer. 


' 


FIG.  306.— Scout. 


Reproduced  by  courtesy  of  Messrs  Boulton  &  Paul. 

FIG.  307. — Passenger. 
Boulton  &  Paul  Machines. 


Facing  page  444. 


GENERAL  TREND  OF  AEROPLANE  DESIGN        445 


^!Sv  LAN  DING  CHASSIS 
Axle  (OR  UNDERCARRIAGE) 


FIG.   308. — Aeroplane  Nomenclature. 


446 


AEROPLANE    DESIGN 


TABLE  LXXIV.— SAFE  LOADS  IN 


Outside 
diam. 

Area. 
Sq.  ins. 

Weight. 
Lbs.  run 
per  ft. 

LENGTHS 
1O     20     30     40     50     60 

SAFE  LOADS 

Inches. 

GAUGE  22.  THICKNESS 

4  ... 

•0415 

•141 

1300 

650 

4OO   !    25O 

150  '   too 

|   ... 

•0635 

•216 

2800 

1800 

1000     650 

400    500 

I   .- 

•0745 

•253 

3400 

2500 

1500    looo 

700  |   5^0 

I 

•0855 

'291 

4000 

3250 

2200     1450 

1000  I   700 

1*   - 

.0965 

•328 

4600 

3850 

2850     1900 

1350    1000 

It  ... 

•1075 

•366 

5100 

4500 

3550     2500 

1800    1300 

i£  ..• 

•Il85 

'403 

5700 

5100 

4250     3150 

2300   1700 

•1295 

•440 

6300 

5750 

4950     3800 

2900    2150 

if  ... 

•1405 

•478 

6850 

6300 

5550   4500  ;  3500   2650 

if  ... 

•1515 

•515 

7400 

6900   6200    5200   4100   3200 

i-g  .- 

•1625 

•553 

8000 

7500   6900   5900  !  4750   3800 

2 

•1735 

•590 

8500 

8050 

7500     6550 

5500   4400 

GAUGE  20.  THICKNESS 

4-  -. 

•0525       -178 

2OOO 

1200 

700 

450 

300 

200 

». 

'0807       '275 

3900 

2500 

1450 

850 

500 

350 

1  ... 

•0949       "323 

4800 

3550 

2200 

1400 

900 

650 

•1090 

•571 

5600 

4500 

3000 

2COO 

1400 

IOOO 

§•  ••• 

•1232 

•419 

6500 

5500 

4OOO 

2750 

1950 

1350 

i  ... 

•'373       ^7 

7300 

6400 

5000 

3600 

2500 

1800 

1  ... 

•I5I4       '515 

8200 

7300 

5950 

45°0 

33oo 

2400 

h  ... 

•1656       .563 

9000 

8200 

6900 

5400 

4000 

3000 

1  ... 

•1797     -611 

9700 

9050 

7900 

6300 

5000 

3800 

•1938     -659 

10600 

9850 

8800 

7300 

5800 

4600 

15  ... 

•2080     .707 

I[400 

10700 

9700 

8400 

6700 

5400 

2 

•2221     .755 

12200 

II500 

10650 

9400 

7800 

6400 

GAUGE  17.  THICKNESS 

\  ... 

•0781     '401 

2000 

1000 

400 

250 

200 

170 

f  ••• 

•1221 

•647 

5900 

3500 

1900 

I  100 

800 

500 

•1441 

"769 

7200 

5600 

3150 

1900 

1150 

800 

... 

•1661 

.892 

,3700 

7000 

4500 

2900 

1950 

1350 

i  ... 

•1881 

•015 

9800 

8250 

6000 

4000 

2800 

2OOO 

i  ... 

•2101 

•I38 

III50 

9850 

7500 

5000 

3700 

2750 

f 

'2321 

•26l 

12600 

1  1200 

9OOO 

t6oo 

475° 

3500 

4  ••• 

•2540 

•384 

13700 

12500 

10600 

8000 

6000 

4500 

1 

•2760 

•507 

14900 

13800 

12100 

9700 

7400 

5600 

f  ... 

•2980 

'629 

16300 

15200 

13700 

11250 

8900 

6900 

I 

•3200 

752 

17600 

16600 

14900 

12750 

10150 

8000 

2 

•3420 

•875 

18800 

17850 

16400 

14250 

11800 

9500 

GENERAL  TREND  OF  AEROPLANE  DESIGN        447 


LBS.  FOR  TUBULAR  STEEL  STRUTS. 


IN  INCHES. 
70      80 

90     1OO     110     120    130    140     15O 

IN  LBS. 

OF  METAL,  0*028" 

80 

70 

60 

5° 

40 

— 

— 

—    1    — 

200 

I  0 

150 

120 

100 

80 

— 

—       — 

35o 

300 

230 

2OO 

150 

120 

100 

—       — 

500 

400 

330 

280 

200 

1  60 

130 

110 

750 

550 

440 

350 

280 

24O 

1  80 

1  60 

150 

1000     8co 

600 

460 

360 

320 

260 

220 

2OO 

1300     1000 

800 

650 

520 

450 

340 

280 

250 

i  700     i  300 

1080 

830 

700 

600 

500 

420 

35-3 

2100 

1650 

1350 

1  100 

870 

750 

650 

560 

500 

2550 

2000 

1650 

1350 

1130 

920 

800 

750 

650 

3000 

2450 

2000 

1700 

I4OO 

1200 

1000 

880 

800 

3600 

29CO 

2400 

2000 

1650 

1400 

1200 

IIOO 

IOOO 

OF  METAL,  0-036' 


| 

150 

100 

90 

80 

70 

• 

— 

—  .       — 

250 

200 

200 

170 

150 

130 

— 

—        — 

500 

350 

300 

280 

230 

200 

180 

— 

— 

700 

550 

450 

4OO 

330 

280 

250 

1  80 

— 

IOOO 

800 

650 

550 

450 

370 

320 

280      250 

1400 

IIOO 

850 

700 

600 

500 

420 

380      300 

1800 

1400 

1150 

900 

800 

650 

550 

500      450 

2300 

1800 

1500 

1200 

IOOO 

850 

800 

700      550 

2800    2300 

1850 

1500 

1300 

IIOO 

920 

800  !   700 

3600    2800 

2300 

1850 

1550 

1300 

1150 

I  ooo     900 

4300   3400 

2950 

2300 

1950 

1650 

1400 

1300 

1150 

5200     4100 

3350 

2750 

2353 

2000 

1700 

1500 

1350 

OF  METAL,  0*056' 


150 

120 

100 

70 







_ 

__ 

350 

250 

200 

120 

100 

— 

— 

•'  

•  — 

too 

500 

4OO 

320 

300 

260 

— 

— 



950 

800 

650 

550 

500 

350 

320 





1500 

1200 

950 

800 

700 

550 

500 

450 



2000 

I600 

1300 

IOOO 

850 

750 

650 

$70 

500 

2700 

2100 

J700 

1400 

1200 

IOOO 

850 

750 

650 

3450 

2700 

22OO 

1800 

1500 

1250 

IOOO 

875 

800 

4300 

3500 

2800 

2300 

1900 

1650 

1350 

TI50 

IOOO 

5300 

4300 

3500 

2850 

2400 

2000 

1700 

1500 

1250 

6500 

5100 

4250 

3550 

2000 

2500 

2100 

1850 

1600 

7700 

6200 

5000 

4200 

3600 

3050 

2600 

2300 

2000 

449 


LIST  OF  TABLES. 


I.    Comparison  of  Calculated  and  Actual  Performance. 
II.   Weights  of  Structural  Components  expressed  as  Percentages 
of  the  Total  Weight. 

III.  Diminution  in  Weight  per  H.P.  of  Aero  Engines. 

IV.  Percentage  Resistance  of  Aeroplane  Components. 
V.    Strength  and  Weight  of  Timbers. 

VI.    Properties  of  Duralumin. 
VII.    Specific  Tenacity  of  Different  Materials. 
VIII.    Steels  to  Standard  Specifications. 
IX.    Brinell  Hardness  Numbers. 
X.    Factors  of  Safety. 
XI.    Wind  Pressures. 
XII.    Table  of  Forces. 

XIII.  Table  of  Forces. 

XIV.  Influence  of  Aspect  Ratio  on  the  Normal  Pressure  of  a  Flat 

Plate  (Eiffel). 
XV.    R.A.F.6.  Coefficients. 
XVI.    Influence  of  Aspect  Ratio. 
XVII.    Camber. 

XVIII.    Reduction  Coefficients  due  to  Biplane  Effects. 
XIX.    Comparison  of  Lift  Coefficients. 

XX.    Comparison  of  the  Wings  of  a  Triplane. 
XXI.    Calculations  of  V/V. 
XXII.    Moments  of  Inertia — Geometrical  Sections. 

XXIII.  Load,  Shear  Force,  Bending  Moment  and  Deflection. 

XXIV.  Shear,  Bending    Moment,    Slope,  and   Deflection  by   Tabular 

Integration. 

XXV.   Wing  Loading  of  Modern  Machines. 
XXVI.    Bracing  Wires  and  Tie-rods. 
XXVII.    Particulars  of  Strands  for  Aircraft  Purposes. 
XXVIII.    Strainers. 

XXIX.    Resistances  of  Struts. 

XXX.    Resistance  Coefficients  for  Fuselage  Shapes. 
XXXI.    Monocoque  Fuselages  without  Airscrews. 
XXXII.    Monocoque  Fuselages  with  Airscrews. 

XXXIII.  Comparison  of  Four  Fuselage  Bodies. 

XXXIV.  Values  of  K  with  Increase  of  dV. 
XXXV.   Resistance  of  Inclined  Struts  and  Wires. 

HH 


45° 


List  of  Tables. 


XXXVI.    Resistances  of  Landing  Wheels. 
XXXVII.  Estimate  of  Body  Resistance  of  B.E.2  at  60  M.P.H. 
XXXVIII.    Resistance  of  Aeroplane  Components. 
XXXIX.   Skin  Frictional  Resistances. 

XL.    Percentage  Weights  of  Aeroplane  Components. 
XLI.    Weights  and  Particulars  of  Leading  Aero  Engines. 
XLII.    Elongation  of  Shock  Absorber. 
XLI  1 1.    Stresses  due  to  Centrifrugal  Force. 
XLIV.    Stresses  due  to  Bending. 

XLV.    Maximum  Stresses  in  the  Airscrew  Blade. 
XLVI.    Stability  Nomenclature. 

XLVII.    (Case  I.)  Speed  79  m.p.h.  Angle  of  Attack  (i)  i° 
XLVIII.    (Case  II.)  Speed  45  m.p.h.  Angle  of  Attack  (i)  12°. 
XLIX.   Wing  Characteristics. 

L.    Determination  of  Angle  of  Downwash. 
LI.  „  „  & 

LI  I.  „  „  Angle  of  Tailplane  tq  Body. 

LI  1 1.  „  „  Elevator  Moment. 

LIV.  „  „  Ky' 

LV.    Lateral  Force  of  Aeroplane  Components. 
LVI.    Determination  of  Wing  Resistance. 
LVII.  „  „   H.P.  available. 

LVI  1 1.    Mean   Atmospheric    Pressure,   Temperature,   and    Density   at 

Various  Heights  above  Sea  Level. 

LIX.    Percentage  of  Standard  Density  due  to  Change  of  Altitude. 
LX.    Calibration  of  an  Airspeed  Indicator  by  Direct  Test. 
LXI.    Airspeed  at  Heights. 
LXII.    Rate  of  Climb  Test. 

LXI  1 1.    Determination  of  the  Position  of  the  Centre  of  Gravity. 
LXIV.    Balancing. 

LXV.    Body  Resistance  (Outside  Slip  Stream). 
LXVI.    Body  Resistance  (In  Slip  Stream). 
LXVII.    Calculation  of  Slip  Stream  Coefficient. 
LXVI  1 1.    Body  Resistance  of  Machine  at  Different  Speeds. 
LXIX.   Calculation  of  Total  Resistance. 

LXX.    Horse-power  Required  and  Available,  and  Rate  of  Climb. 
LXXI.    Progress  of  Civil  Aviation  in  England,  May  I5th  to  October  31  st, 

1919. 
LXXI  I.    Data  relating  to  Successful  Aeroplanes. 

LXXI  Hi  ..  ,,  ,,  ;, 

LXXIV.    Safe  Loads  in  Ibs.  for  Tubular  Steel  Struts. 


.451 


INDEX. 


A   CCELEROMETER,  145. 
2~\.     Aeroplane  nomenclature,  445. 
Aerodynamic  balance,  41-45. 
Aero  engines,  239. 
Aerofoil,  38,  et  seq. 

—  characteristics,  3,  50,  59. 
choice,  84-86. 

comparison  with  model,  64. 

effect  of  thickening  L.  E.,  73. 

„  „  T.  E.,  74- 

full-scale  pressure  distribution,  62, 

63- 

pressure  distribution,  55,  57,  60,  61. 

superimposed,  79,  80. 

upper  and  lower  surfaces  compared, 

65,66. 
variation  of  maximum  ordinate,  71, 

72. 
Ailerons  (wing  flaps),  372. 

—  balanced,  377. 
Airco  machines,  429,  430. 
Airscrew,  7,  280,  et  seq. 

—  airscrew  balance,  302. 
angle  of  attack,  9. 

—  construction,  299. 

—  design,  285,  286,  295,  296. 
efficiency,  8,  140,  287,  289. 

—  slip  ratio,  282,  283. 

stresses,  295-98. 

testing,  302. 

variable  pitch,  9. 

Airspeed  indicator,  390,  392. 

calibration,  401. 

Altimeter,  398,  399. 
Alloys,  light,  15. 

—  steel,  17. 
Anemometer,  390. 
Aneroid  barometer,  397,  398. 
Angular  accelerations,  308. 
Armstrong  -  Whitworth    machines,    137, 

428,  431. 

Aspect  ratio,  5,  47-49,  63-65,  382,  383. 
Atlantic  flight,  425. 
Australian  flight,  425. 


120,   121, 


Avro  biplane,  421. 

Avro  machines,  426,  et  seq. 

Avro  triplane,  426. 

BANKING,  143. 
Bairstow,  304,  313,  333. 
Bending  moment,  110-13,  IJ8, 

198. 

B.E.  2  biplane,  349. 
B.E.  2  fuselage. 
B.E.  3  fuselage,  222-27. 
Bernouilli's  assumption,  144,  155. 
Biplane,  5,  80. 

strutless,  135. 

trusses,  132. 

wireless,  134. 

Blade  element  theory,  280,  490,  et  seq. 
Bleriot,  131,  425,  426. 

stability  model,  315,  321,  323,  335. 

Body  resistance,  213,  383,  386,  417,419. 
Boulton  &  Paul  machines,  437,  444. 
Bow's  notation,  28. 
Brinell  hardness,  22,  23. 
Bristol  fighter,  146,  147. 

machines,  431,  432. 

monoplane,  424. 

triplane,  433. 

Bryan,  304. 
Bulk  modulus,  21. 

/CAMBER,    upper   service    variable, 
\^     67-69. 

lower  service  variable,  70. 

Ceiling,  8. 

Centre  of  gravity,  75,  132,  257,  260,  410. 

Centre  of  pressure,  16,  74,  75,   149,  160, 

162,  3^6,  374. 

Centre  of  resistance,  414,  417,  418. 
Chanute,  I,  132. 
Chassis,  260. 

design,  262,  et  seq. 

location,  261,  262. 

resistance,  230. 


452 


Index. 


Chassis,  stresses,  269-71. 

types,  264,  269. 

Civil  aviation,  425. 
Clerk  Maxwell,  26. 
Controllability,  5,  9,  n,  303,  346. 
Control  surfaces,  346,  et  seq.,  443. 

balanced,  375. 

Controls,  407. 

Cowling,  255. 

Curtiss,  253. 

stability  model,  339-44. 

DECALAGE,  83. 
Deflexion,  118,  120,  121. 
De  Havilland,  429. 
Density,  standard,  390. 
Derivatives,  resistance,  301,  314. 

rotary,  304,  314. 

Dihedral,  407. 

Dines,  389. 

Down-loading  stresses,  151,  155-57,  165, 

197. 

Drag,  4,  7,  49-52,  54,  58. 
Drag-bracing,   137,   138,   163,   177,   191, 

194. 

Drag-struts,  177,  178,  195. 
Drawings,  general  scheme,  411. 
Dual  control,  378. 
Duplication,  161. 
Duralumin,  15. 

T^  CCENTRIC  loading,  126. 

j"j     Eddy  motion,  59. 
Eiffel,  38,  47,  231. 
Eiffel  laboratory,  45,  46. 
Elasticity,  20. 
Elevator,  346,  356,  379. 

settings,  359,  et  seq. 

End  effect,  62,  287. 
End  correction  factor,  198. 
Engine  mountings,  250-53. 
Equations  of  motion,  307. 
Equivalent  chord,  357. 
Euler's  formula,  125,  126. 

FABRIC,  20. 
Factor  of  safety,  23,  24,  140,  141. 
Farman,  H.,  132. 
Fin,  368,  379. 
Fineness  ratio,  129. 
Flat  plate,  force  on,  47. 

inclined,  48. 

edgewise,  50. 

resistance,  230. 

Forces,  10. 

Fuselage  design,  237,  et  seq. 

monocoque,  223,  238,  245,  443. 

resistance,  213,  215-20,  222. 

stressing,  247,  249. 


AP,  77,  407- 

Grieve,  425. 
Gyroscopic  action,  257-59. 

Handley  Page,  424,  425,  433,  434. 

fuselage,  245. 

Hanging  on  the  prop,  8. 
Hawker,  433,  435. 
Hooke's  law,  21,  114. 
Horse-power,  7. 

available,  384,  424,  487. 

required,  384,  487,  420. 

T  NCIDENCE  bracing,  137,  138,  162. 

1      Incidence  gears,  363,  379. 
Inherently  stable,  303. 
Interference,  77,  383. 
Interplane    struts,     165,     171-76,     178, 
184-91. 

Tx-INEMATIC  viscosity,  89. 

LANCHESTER,    304. 
Langley,  48,  424. 
Lateral  force,  319,  325,  327,  370. 

in  airscrew,  372. 

Lay-out,  403,  et  seq. 

Leading  edge,  73. 

Lift,  4,  7,  49-52,  54,  58. 

effect  of  variable  camber  on,  68-71. 

—  bracing,  165. 
Lift/Drag,  51,  53,  54. 

superimposed  aerofoils,  83. 

Lilienthal,  i. 

Linear  accelerations,  307. 

Load,  118,  122,  27. 

—  diagram,  122. 
Longitudinal  force,  317,  353,  354. 

MATERIALS,  13,  et  seq. 
Maxim,  424. 

Meridian  curve  (tapered  strut),  174. 
Method  of  sections,  35-37. 
Moments  of  inertia,  101,  102,  105-108^ 
Monoplane,  5,  80. 

trusses,  130. 

Multiplane,  6. 

NIEUPORT,  6,  133,  139. 
Nomograms,  1 08,  109. 
Normal  force,  318,  352,  355. 
Nose  diving,  144. 
National  Physical  Laboratory,  38. 

OLEO  gear,  276. 
Oscillations,  longitudinal,  315. 
lateral,  313. 


Index. 


453 


TT)ARALLEL  axes,  102. 
\^      Parasol  type,  132. 
Performance,  2,  381,  et  seq.,  389,  444. 

• curves,  421. 

test,  full  scale,  395. 

Perry  formula,  129. 
Pfalz,  248. 
Pitching,  305. 

—  moment,  319,  254,  352,  355. 
Pitot  tube,  56,  392,  393. 
Poisson's  ratio,  21,  22. 
Polar  moment  of  inertia,  105. 
Polygon  offerees,  26. 
Pratt  truss,  131,  132. 
Pusher,  139,  176,  254. 

^vUADRUPLANE  trusses,  137. 

T~)  ADIATORS,  255-57. 

\\_    R.A.F.  6,  characteristics,  54,  164. 

R.A.F.  wires,  167 

Rankine-Gordon  formula,   126,  127,  249, 

250. 

Rate  of  climb,  386,  3)6,  400,  402,  421. 
Rayleigh,  88. 
Resistance,  6,  208,  et  seq, 

aeroplane  components,  233. 

• complete  machine,  232. 

wires,  228,  229,  382,  420. 

Ribs,  177,  203-206. 
Rigidity  modulus,  21. 
Rolling,  305. 

moment,  320,  325,  327. 

Ross-Smith,  425. 

Routh's  discriminant,  313,  330,  343. 

Rudder,  368,  379,  408. 


SECTION  modulus,  116. 
S.  E.  4.  369- 
S.  E.  5,  145,  146,  442. 
Shear  force,  110-13,  I9%- 
Shear  stress,  116,  118. 
Shock  absorbers,  272-76. 
Similitude,  88. 

Skin  friction,  209,  234-37,  244. 
Slip  stream,  air-screw,  231., 

—  coefficient,  234,  419. 
Slope,  118,  120,  121. 
Sopwith  machines,  433,  435. 
Spars,  179,  181,  195,  196,  199,  200,  201. 
Specific  tenacity,  15. 
Spiral  instability,  334. 
Stability,  9,  1 1,  303,  et  seq.,  346,  408. 
nomenclature,  305. 

-  lateral,  319-21,  323,  333. 

longitudinal,  315-17,  330,  338. 

Stable  machine,  303. 


Stagger,  83,  84,  164,  383,  407. 

Stanton,  Dr.,  47. 

Statoscope,  400. 

Steel,  16. 

Strain,  20,  101,  et  seq. 

Strainers,  169,  170. 

Stream  lining,  208,  et  seq. 

chassis,  279. 

Stress,  20,  101,  et  seq.,  148. 

airscrew,  295. 

beams,  1 14. 

chassis,  269-  71. 

fuselage,  247,  249. 

Stress  diagrams,  26,  34. 

reciprocal  figures,  35. 

Struts,  121,  123,  124. 

tapered,   121,  174-76,  184-87,  189, 

191. 

stream  line,  129. 

interplane,  165,  171-74. 

inclined,  213,  229. 

Strut  resistance,  213,  214. 
Sturtevant,  246,  253. 
Superimposed  aerofoils,  79,  80. 


TABULAR  integration,  120. 
Tail-plane   incidence   gears,    363, 

379- 
Tail  plane,  80,  346,  379. 

design,  357. 

interference,  80. 

loading,  347. 

skid,  277,  278. 

Theorem  of  three  moments,  113,  154,  155. 
Tie  rods,  167,  168. 
Timber,  13,  14. 

seasoning,  13. 

Torque,  286. 
Tractive  power,  289. 

airscrew,  231. 

Tractor,  139,  176. 
Trailing  edge,  74. 

—  reflexure,  76,  77. 

Triangle  of  forces,  26. 
Triplane,  5,  80. 
Trusses,  136. 
Thrust,  288,  293. 


u 


NITS,  87, 


VENTURI  meter,  393,  394. 
Vickers  Vimy-Rolls,  425,  432,  436, 

437- 
Vimy  bomber,  240. 

commercial,  244,  245,  248,  432. 

V.  squared  law,  210. 


454 

WASH  from  main  planes,  349. 
Weight,  2,  238. 
Wind  pressure,  24,  25. 

—  tunnel,  38-40. 
Wing  assembly,  206,  207. 
design,   130,  et  seq.,  160,   183,  184, 

443- 

folding,  8,  208. 

resistance,  384,  419. 

sections  and  characteristics,  90-100. 

stresses,  148,  152,  153. 

structures,  130. 

tip  losses,  287. 


Index. 


Wings,  loading,  149,  150. 

-  pressure  distribution,  62,  63. 

-  weights,  149. 
Wires  resistance,  228,  229. 
Wright  brothers,  424,  425. 

—  glider,  8. 


AWING,  305- 
JL       -  moment,  324,  326,  328,  369. 
Young's  modulus,  21,  114. 


235. 


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